Updated on 2022/10/01

写真a

 
SHIMIZU, Yasutaka
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

  • Faculty of Commerce   Graduate School of Accountancy

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Education

  • 2001.04
    -
    2005.03

    The University of Tokyo   Graduate School of Mathematical Sciences  

  • 1995.04
    -
    1999.03

    The University of Tokyo   Faculty of Science   Department of Mathematics  

Degree

  • 2007.10   The University of Tokyo   Ph.D. (in Mathematical Science) by dissertation

Research Experience

  • 2017.04
    -
     

    Full Professor, Department of Applied Mathematics, Waseda University

  • 2014.04
    -
    2017.03

    Associate Professor, Department of Applied Mathematics, Waseda University

  • 2011.10
    -
    2014.03

    Associate Professor, Graduate School of Engineering Science, Osaka University

  • 2007.04
    -
    2011.09

    Assistant Professor, Graduate School of Engineering Science, Osaka University

  • 2005.04
    -
    2007.03

    Research Associate, Graduate School of Engineering Science, Osaka University

  • 1999.04
    -
     

    Dai-ichi Life Insurance co.

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Professional Memberships

  •  
     
     

    日本保険・年金リスク学会

  •  
     
     

    日本統計学会

  •  
     
     

    日本数学会

 

Research Areas

  • Statistical science

  • Basic mathematics

  • Applied mathematics and statistics

  • Money and finance

  • Economic statistics

Research Interests

  • mathematical statistics

  • asymptotic inference

  • stochastic processes

  • 金融・保険数理

Papers

  • Why Does a Human Die? A Structural Approach to Cohort-Wise Mortality Prediction under Survival Energy Hypothesis

    Yasutaka Shimizu, Yuki Minami, Ryunosuke Ito

    ASTIN Bulletin   51 ( 1 ) 191 - 219  2021.01

     View Summary

    We propose a new approach to mortality prediction under survival energy hypothesis (SEH). We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero. This study assumes that SE follows a time-inhomogeneous diffusion process and defines the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is a fictitious construct, we illustrate that this assumption has the potential to yield a good parametric family of cumulative probability of death, and the parametric family yields surprisingly good predictions for future mortality rates.

    DOI

  • Asymptotically normal estimators of the ruin probability for Lévy insurance surplus from discrete samples

    Yasutaka Shimizu, Zhimin Zhang

    Risks   7 ( 2 )  2019.06

     View Summary

    A statistical inference for ruin probability from a certain discrete sample of the surplus is discussed under a spectrally negative Lévy insurance risk. We consider the Laguerre series expansion of ruin probability, and provide an estimator for any of its partial sums by computing the coefficients of the expansion. We show that the proposed estimator is asymptotically normal and consistent with the optimal rate of convergence and estimable asymptotic variance. This estimator enables not only a point estimation of ruin probability but also an approximated interval estimation and testing hypothesis.

    DOI

  • Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data

    Kenichi Hayashi, Yasutaka Shimizu

    Statistics in Biosciences   10 ( 3 ) 546 - 567  2018.12

     View Summary

    Evaluating the relationship between a response variable and explanatory variables is important to establish better statistical models. Concordance probability is one measure of this relationship and is often used in biomedical research. Concordance probability can be seen as an extension of the area under the receiver operating characteristic curve. In this study, we propose estimators of concordance probability for time-to-event data subject to double censoring. A doubly censored time-to-event response is observed when either left or right censoring may occur. In the presence of double censoring, existing estimators of concordance probability lack desirable properties such as consistency and asymptotic normality. The proposed estimators consist of estimators of the left-censoring and the right-censoring distributions as a weight for each pair of cases, and reduce to the existing estimators in special cases. We show the statistical properties of the proposed estimators and evaluate their performance via numerical experiments.

    DOI

  • Dynamic risk measures for stochastic asset processes from ruin theory

    Yasutaka Shimizu, Shuji Tanaka

    Annals of Actuarial Science   12 ( 2 ) 211 - 232  2018.09

     View Summary

    This article considers a dynamic version of risk measures for stochastic asset processes and gives a mathematical benchmark for required capital in a solvency regulation framework. Some dynamic risk measures, based on the expected discounted penalty function launched by Gerber and Shiu, are proposed to measure solvency risk from the company's going-concern point of view. This study proposes a novel mathematical justification of a risk measure for stochastic processes as a map on a functional path space of future loss processes.

    DOI

  • Parametric inference for ruin probability in the classical risk model

    Takayoshi Oshime, Yasutaka Shimizu

    Statistics and Probability Letters   133   28 - 37  2018.02

     View Summary

    Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability.

    DOI

  • Threshold Estimation for Stochastic Processes with Small Noise

    Yasutaka Shimizu

    Scandinavian Journal of Statistics   44 ( 4 ) 951 - 988  2017.12

     View Summary

    Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.

    DOI

  • Least squares estimators for stochastic differential equations driven by small Lévy noises

    Hongwei Long, Chunhua Ma, Yasutaka Shimizu

    Stochastic Processes and their Applications   127 ( 5 ) 1475 - 1495  2017.05

     View Summary

    We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

    DOI

  • Estimating Gerber-Shiu functions from discretely observed Levy driven surplus

    Yasutaka Shimizu, Zhimin Zhang

    INSURANCE MATHEMATICS & ECONOMICS   74   84 - 98  2017.05  [Refereed]

     View Summary

    Consider an insurance surplus process driven by a Levy subordinator, which is observed at discrete time points. An estimator of the Gerber-Shiu function is proposed via the empirical Fourier transform of the Gerber-Shiu function. By evaluating its mean squared error, we show the L-2-consistency of the estimator under the assumption of high-frequency observation of the surplus process in a long term. Simulation studies are also presented to show the finite sample performance of the proposed estimator. (C) 2017 Elsevier B.V. All rights reserved.

    DOI

  • Applications of central limit theorems for equity-linked insurance

    Runhuan Feng, Yasutaka Shimizu

    Insurance: Mathematics and Economics   69   138 - 148  2016.07

     View Summary

    In both the past literature and industrial practice, it was often implicitly used without any justification that the classical strong law of large numbers applies to the modeling of equity-linked insurance. However, as all policyholders' benefits are linked to common equity indices or funds, the classical assumption of independent claims is clearly inappropriate for equity-linked insurance. In other words, the strong law of large numbers fails to apply in the classical sense. In this paper, we investigate this fundamental question regarding the validity of strong laws of large numbers for equity-linked insurance. As a result, extensions of classical laws of large numbers and central limit theorem are presented, which are shown to apply to a great variety of equity-linked insurance products.

    DOI

  • Potential measures for spectrally negative Markov additive processes with applications in ruin theory

    Runhuan Feng, Yasutaka Shimizu

    INSURANCE MATHEMATICS & ECONOMICS   59   11 - 26  2014.11  [Refereed]

     View Summary

    The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems. (C) 2014 Elsevier B.V. All rights reserved.

    DOI

  • The YUIMA project: A computational framework for simulation and inference of stochastic differential equations

    Alexandre Brouste, Masaaki Fukasawa, Hideitsu Hino, Stefano M. Iacus, Kengo Kamatani, Yuta Koike, Hiroki Masuda, Ryosuke Nomura, Teppei Ogihara, Yasutaka Shimuzu, Masayuki Uchida, Nakahiro Yoshida

    Journal of Statistical Software   57 ( 4 ) 1 - 51  2014

     View Summary

    The YUIMA Project is an open source and collaborative effort aimed at developing the R package yuima for simulation and inference of stochastic differential equations. In the yuima package stochastic differential equations can be of very abstract type, multidimensional, driven by Wiener process or fractional Brownian motion with general Hurst parameter, with or without jumps specified as Ĺevy noise. The yuima package is intended to offer the basic infrastructure on which complex models and inference procedures can be built on. This paper explains the design of the yuima package and provides some examples of applications.

    DOI

  • Edgeworth type expansion of ruin probability under Levy risk processes in the small loading asymptotics

    Yasutaka Shimizu

    SCANDINAVIAN ACTUARIAL JOURNAL   2014 ( 7 ) 620 - 648  2014  [Refereed]

     View Summary

    This paper presents an asymptotic expansion of the ultimate ruin probability under Levy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Levy processes.

    DOI

  • On a Generalization from Ruin to Default in a Lévy Insurance Risk Model

    Runhuan Feng, Yasutaka Shimizu

    Methodology and Computing in Applied Probability   15 ( 4 ) 773 - 802  2013.12

     View Summary

    In a variety of insurance risk models, ruin-related quantities in the class of expected discounted penalty function (EDPF) were known to satisfy defective renewal equations that lead to explicit solutions. Recent development in the ruin literature has shown that similar defective renewal equations exist for a more general class of quantities than that of EDPF. This paper further extends the analysis of this new class of functions in the context of a spectrally negative Lévy risk model. In particular, we present an operator-based approach as an alternative analytical tool in comparison with fluctuation theoretic methods used for similar quantities in the current literature. The paper also identifies a sufficient and necessary condition under which the classical results from defective renewal equation and those from fluctuation theory are interchangeable. As a by-product, we present a series representation of scale function as well as potential measure in terms of compound geometric distribution. © 2012 Springer Science+Business Media, LLC.

    DOI

  • Finite-time survival probability and credit default swaps pricing under geometric Levy markets

    Xuemiao Hao, Xuan Li, Yasutaka Shimizu

    INSURANCE MATHEMATICS & ECONOMICS   53 ( 1 ) 14 - 23  2013.07  [Refereed]

     View Summary

    We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short. (C) 2013 Elsevier B.V. All rights reserved.

    DOI

  • Least squares estimators for discretely observed stochastic processes driven by small Levy noises

    Hongwei Long, Yasutaka Shimizu, Wei Sun

    JOURNAL OF MULTIVARIATE ANALYSIS   116   422 - 439  2013.04  [Refereed]

     View Summary

    We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Levy noises. We do not impose any moment condition on the driving Levy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient epsilon -> 0 and n -> infinity simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Levy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises. (C) 2013 Elsevier Inc. All rights reserved.

    DOI

  • Estimation of parameters for discretely observed diffusion processes with a variety of rates for information

    Yasutaka Shimizu

    Annals of the Institute of Statistical Mathematics   64 ( 3 ) 545 - 575  2012.06

     View Summary

    A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities. © 2010 The Institute of Statistical Mathematics, Tokyo.

    DOI

  • Non-parametric estimation of the Gerber-Shiu function for the Wiener-Poisson risk model

    Yasutaka Shimizu

    Scandinavian Actuarial Journal   ( 1 ) 56 - 69  2012.03

     View Summary

    A non-parametric estimator of the Gerber-Shiu function is proposed for a risk process with a compound Poisson claim process plus a diffusion perturbation; the Wiener-Poisson risk model. The estimator is based on a regularized inversion of an empirical-type estimator of the Laplace transform of the Gerber-Shiu function. We show the weak consistency of the estimator in the sense of an integrated squared error with the rate of convergence. © 2012 Taylor and Francis Group, LLC.

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  • Local asymptotic mixed normality for discretely observed non-recurrent Ornstein-Uhlenbeck processes

    Yasutaka Shimizu

    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS   64 ( 1 ) 193 - 211  2012.02  [Refereed]

     View Summary

    Consider non-recurrent Ornstein-Uhlenbeck processes with unknown drift and diffusion parameters. Our purpose is to estimate the parameters jointly from discrete observations with a certain asymptotics. We show that the likelihood ratio of the discrete samples has the uniform LAMN property, and that some kind of approximated MLE is asymptotically optimal in a sense of asymptotic maximum concentration probability. The estimator is also asymptotically efficient in ergodic cases.

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  • Estimation of the expected discounted penalty function for Lévy insurance risks

    Y. Shimizu

    Mathematical Methods of Statistics   20 ( 2 ) 125 - 149  2011.06

     View Summary

    We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated. © 2011 Allerton Press, Inc.

    DOI

  • Threshold selection in jump-discriminant filter for discretely observed jump processes

    Yasutaka Shimizu

    STATISTICAL METHODS AND APPLICATIONS   19 ( 3 ) 355 - 378  2010.08  [Refereed]

     View Summary

    Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this method, a jump-discriminant filter is used to infer the continuous part and the jump part separately. Although there are several choices for the filter, statistics constructed via filters are often sensitive to the choice. This paper presents some numerical procedures for selecting a suitable filter based on observations.

    DOI

  • Notes on drift estimation for certain non-recurrent diffusion processes from sampled data

    Yasutaka Shimizu

    Statistics and Probability Letters   79 ( 20 ) 2200 - 2207  2009.10

     View Summary

    Given discrete samples from Ornstein-Uhlenbeck processes, we consider two kinds of approximated MLE's for the drift parameter, which are asymptotically efficient in ergodic case. Our interest is the rate of convergence of those estimators when the process is non-recurrent. We add a remark when the underlying process has a slightly more general drift. © 2009 Elsevier B.V. All rights reserved.

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  • A new aspect of a risk process and its statistical inference

    Yasutaka Shimizu

    Insurance: Mathematics and Economics   44 ( 1 ) 70 - 77  2009.02

     View Summary

    We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the process does not necessarily correspond to the each claim size. Therefore our risk process is different from the traditional risk process. We cannot directly observe each jump size because of discrete observations. Our goal is to estimate the adjustment coefficient of our risk process from discrete observations. © 2008 Elsevier B.V. All rights reserved.

    DOI

  • Model selection for Levy measures in diffusion processes with jumps from discrete observations

    Yasutaka Shimizu

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   139 ( 2 ) 516 - 532  2009.02

     View Summary

    We deal with parametric inference and selection problems for jump components in discretely observed diffusion processes with jumps. We prepare several competing parametric models for the Levy measure that might be misspecified. and select the best model from the aspect of information criteria. We construct quasi-information criteria (QIC), which are approximations of the information criteria based on continuous observations. (C) 2008 Elsevier B.V. All rights reserved.

    DOI

  • 飛躍型確率過程に対する離散観測による閾値推定法

       2009

  • Functional estimation for Lévy measures of semimartingales with Poissonian jumps

    Journal of Multivariate Analysis   100  2009

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  • Thereshold estimation for jump-type stochastic processes from discrete observations

       2009

  • Statistical specification of jumps under semiparametric semimartingale models

    Ya. Shimizu

    Mathematical Methods of Statistics   17 ( 3 ) 209 - 227  2008.09

     View Summary

    We consider a semimartingale with jumps that are driven by a finite activity Lévy process. Suppose that the Lévy measure is completely unknown, and that the jump component has a Markovian structure depending on unknown parameters. This paper concentrates on estimating the parameters from continuous observations under the nonparametric setting on the Lévy measure. The estimating function is proposed by way of nonparametric approach for some regression functions. In the end, we can specify jumps of the underlying Lévy process and estimate some Lévy characteristics jointly. © 2008 Allerton Press, Inc.

    DOI

  • A PRACTICAL INFERENCE FOR DISCRETELY OBSERVED JUMP-DIFFUSIONS FROM FINITE SAMPLES

    Yasutaka Shimizu, Division of Mathematical Science Graduate School of Engineering Science Osaka University

    Journal of the Japan Statistical Society   38 ( 3 ) 391 - 413  2008

     View Summary

    In the inference for jump-diffusion processes, we often need to get the information of the jump part and of the continuous part separately from the data. Although some asymptotic theories have been studied on this issue, a practical interest is the inference from finitely many discrete samples. In this paper we propose a numerical procedure to construct a filter to judge whether or not a jump occurred from finite samples. The paper includes a discussion about the validity of the procedure.

    DOI CiNii

  • Some remarks on estimation of diffusion coefficients for jump-diffusions from finite samples

    Bulletin of Informatics and Cybernetics    2008

  • Consistency of penalized risk of boosting methods in binary classification

    New Trends in Psychometrics   87-96  2008

  • Estimation of parameters for diffusion processes with jumps from discrete observations

    Yasutaka Shimizu, Nakahiro Yoshida

    Statistical Inference for Stochastic Processes   9 ( 3 ) 227 - 277  2006.10

     View Summary

    In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure q θ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe n+1 data at t i n = ih n, 0 ≤ i ≤ n. We suppose h n → 0, nh n → ∞, nh n 2 → 0. © Springer 2006.

    DOI

  • M-estimation for discretely observed ergodic diffusion processes with infinitely many jumps

    Yasutaka Shimizu

    Statistical Inference for Stochastic Processes   9 ( 2 ) 179 - 225  2006.07

     View Summary

    We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f θ(z)dz, and we admit the case f θ(z)dz=∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models. © Springer 2006.

    DOI

  • Density Type Estimation of Levy Densities for Discretely Observed DiffusionProcesses with Jumps

    Journal of Japan Statistical Society   36, no.1, 37-62  2006

    DOI

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Books and Other Publications

  • Asymptotic Statistics in Insurance Risk Theory

    Yasutaka Shimizu( Part: Sole author)

    Springer  2022.01

  • 統計学への確率論, その先へ (第2版)

    清水, 泰隆

    内田老鶴圃  2021.07 ISBN: 9784753601257

  • 市場整合的ソルベンシー評価 : 金融リスクとアクチュアリアル・モデリング

    Wüthrich, Mario V, Merz, Michael, 田中, 周二, 清水, 泰隆

    共立出版  2020.08 ISBN: 9784320096493

  • 統計学への確率論,その先へ : ゼロからの測度論的理解と漸近理論への架け橋

    清水, 泰隆

    内田老鶴圃  2019.04 ISBN: 9784753601257

  • 保険数理と統計的方法

    清水, 泰隆

    共立出版  2018.10 ISBN: 9784320113510

  • Asymptotic inference for stochastic differential equations with jumps from discrete observations and some practical approaches = 飛躍型確率微分方程式に対する離散的観測に基づく漸近推測理論, 及びその実際的方法

    清水, 泰隆

    東京大学数理科学研究科  2009

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Awards

  • 小川研究奨励賞

    2007.09   日本統計学会  

  • コンペティション優秀報告賞

    2004.09   日本統計学会  

Research Projects

  • ジャンプを含む確率過程の複雑な観測データに対する統計解析と新しい学習理論への応用

    日本学術振興会  科学研究費助成事業 基盤研究(B)

    Project Year :

    2021.04
    -
    2026.03
     

    荻原 哲平, 清水 泰隆, 深澤 正彰, 上原 悠槙

  • 一般化確率変数の期待値型汎関数に対する推測誤差への漸近分布論的アプローチ

    日本学術振興会  科学研究費助成事業 基盤研究(C)

    Project Year :

    2021.04
    -
    2024.03
     

    清水 泰隆

  • 確率微分方程式モデルに基づく数理・データ科学とシミュレーション科学の融合的研究

    日本学術振興会  科学研究費助成事業 基盤研究(A)

    Project Year :

    2017.04
    -
    2022.03
     

    内田 雅之, 清水 泰隆, 林 高樹, 小池 祐太

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    今年度は,(i) 観測ノイズ付きエルゴード的拡散過程のハイブリッド型推測法の開発,(ii) Determinantal Point Process(DPP) の統計的推測および確率過程を用いた新しい死亡率予測のモデリング,(iv) 高頻度時系列データに基づく高次元共分散行列の統計推測,(v) 先行遅行関係の推定手法について研究を行った.詳細は次の通りである.(i) エルゴード的拡散過程から得られた観測ノイズ付きの高頻度データを用いて,初期ベイズ型推定量およびハイブリッド型推定量を導出し,その漸近的性質を証明した.(ii) DPPに対するある種の疑似尤度を用いたM-推定量に対する漸近正規性とその十分条件を与え,それに基づく情報量規準の構成を行った.また,人間の死亡時刻の分布が,拡散過程の初期到達時刻(停止時刻)によって近似できるという実証を与え,その理論式によって死亡時刻の分布のパラメトリック族を与え,確率微分方程式のパラメータ推定とその推移予測を通して死亡率予測を行った.(iii) 高次元高頻度データの精度行列(共分散行列の逆行列) に対する統計推測について研究した. 独立同一分布データにおいて精度行列を推定するための標準的な手法の1 つであるgraphical Lasso が, 金融高頻度データ解析の文脈でも正当化できることを示した.(iv) リード・ラグ関係の統計的有意性を検定する検定統計量の帰無分布を導出するために必要となる,多数の二次形式の最大値の分布を,Gauss過程の最大値で近似するための漸近理論を構築した.また,NASDAQ100指数の構成銘柄の異市場間での気配値間の先行遅行分析を行い,異なる時間スケールにおいて異なる種類の先行遅行関係が観察されることを確認した.観測ノイズ付きエルゴード的拡散過程のパラメトリック推測問題に対して,高頻度データから局所平均を算出して,縮小および間引きされた局所平均から,最適収束率を有しないが計算時間が短く比較的安定した初期ベイズ型推定量を導出した.具体的には,ボラテリティパラメータに対しては縮小データに基づくベイズ型推定量を導出し,ドリフトパラメータに対しては,間引きデータに基づくベイズ型推定量を構成した.その後,Kaino and Uchida (2018:SISP)で提案された間引きデータに基づいたマルチステップ推定法を応用して,ノイズ付きエルゴード的拡散過程モデルのハイブリッド型推定量を導出した.そして,観測ノイズ付き拡散過程に対する疑似尤度解析を整備して,観測ノイズ付き拡散過程に対するベイズ型推定量やハイブリッド型推定量の漸近的性質を証明した.本研究は初期ベイズ型推定量が重要な役割を果たすため,確率微分方程式のベイズ型推定量の算出のためのプログラムを開発して,大規模数値シミュレーションを実行し,提案した推定量の漸近挙動を検証した. 観測ノイズ付きエルゴード的拡散過程におけるハイブリッド型推定法を開発したことにより,最尤型推定量に比べて,数値的に安定した推定量を導出することが可能となった.これまでの研究によって,エルゴード的拡散過程や非エルゴード的拡散過程,観測ノイズ付き拡散過程に対して,高頻度データに基づく適合型推測法やハイブリッド型推測法が有効であることがわかった.今後は確率微分方程式モデルの適応型変化点検出問題や適応型統計的仮説検定問題に取り組む.具体的には,高頻度データに基づいてエルゴード的拡散過程のボラテリティパラメータやドリフトパラメータの変化を検出するために,最初にボラテリティパラメータに対する擬似尤度関数を用いて,ボラテリティパラメータの変化を検出するための検定統計量を導出する.ボラティリティパラメータに変化がなかった場合は,ドリフトパラメータに対する擬似尤度関数として,ボラティリティパラメータの推定量を代入した適応型擬似尤度関数を用いて,ドリフトパラメータの変化を検出するための適応型検定統計量を構成する.そして,得られた適応型検定統計量の漸近分布などの漸近的性質を証明する.さらに,計算機による大規模数値シミュレーションにより,提案した適応型検定統計量の漸近挙動を検証して,エルゴード的拡散過程の変化点検出問題や統計的仮説検定問題のための適応型検定法の有効性を確認する

  • New developments of statistical methods for risk management in finance and insurance

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2018.04
    -
    2021.03
     

  • Theory for quantile regression inference of time series and its applications

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

    Project Year :

    2015.04
    -
    2019.03
     

    Taniguchi Masanobu, Hallin Marc, Monti Anna Clara

     View Summary

    (1)We introduced a quantile regression statistic to classify time series data into a certain category. Results show that the misclassification probability of the discriminant statistic converges to zero as the sample size tends to infinity. We applied the proposed method in quantile autoregression to a dataset of the monthly mean maximum temperature at Melbourne.The findings illuminate interesting features of climate change and allow us to check the change at each quantile of the innovation distribution.(2)We considered minimax interpolation and extrapolation problems in Lp for stationary processes. We gave two conditions to find the minimax interpolator and extrapolator in the general framework under the Lp-norm. We showed that there exist minimax interpolator and extrapolator for the class of epsilon contaminated spectral densities.The results (1) and (2) open a new methodology for time serires analysis based on quantile informations for probability and spectral distributions.

  • Research on statistical solvency estimates from ruin theory

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :

    2015.04
    -
    2018.03
     

    Shimizu Yasutaka

     View Summary

    We constructed a risk measure based on the ruin probability and the Gerber-Shiu function, which is a generalization of the ruin probability, under the surplus model by stochastic differential equation with jumps. In particular, we considered “dynamic” risk measures in order to measure risks that varies in time with their mathematical justification. Next, we investigated a mortality prediction model for the purpose of including a mortality risk into our risk measure. We proposed a new methodology to improve the small area estimation of mortality by applying Credibility Theory. However the performance of the method is not satisfactory and we will leave it as a future work. Furthermore we investigated the statistical inference for the Gerber-Shiu function, which is necessary for application of risk measures in practice

  • Ultra high frequency data and lead-lag

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research

    Project Year :

    2014.04
    -
    2017.03
     

    Yoshida Nakahiro, MASUDA Hiroki, UCHIDA Masayuki, SHIMIZU Yasutaka, KAMATANI Kengo, HAYASHI Takaki

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    An estimator for correlation between two intensity processes was proposed and limit theorems were proved when the intensities diverge under finite time horizon. These results form the basis for lead-lag estimation and price modeling. For a point process regression model, we constructed Quasi Likelihood Analysis based on statistical random fields and polynomial type large deviation inequalities, especially in long-term asymptotics. Models of limit order book dynamics were proposed and fitted to real data

  • New Developments in Statistics of Economic Risk and Financial Risk

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

    Project Year :

    2013.04
    -
    2017.03
     

    naoto kunitomo, KUSUOKA Sigeo, ICHIBA Tomoyuki

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    This research project has studied important issues of economic risk analysis including financial risk and insurance risk in modern society and economy. We have studied various scientific and systematic aspects of economic risk analysis the perspective of probability as well as statistics. The project members have presented research results at various international as well as domestic academic meetings, and published some books and many academic papers.For financial risk and insurance risk analysis we have investigated the statistical risk theory and mathematical finance. For economic risk, we have investigated the point process approach, which would make a new risk analysis of economic rare events. We also made some progress on the consistent statistical analysis of micro analysis (or high frequency risk analysis) and macro analysis (or low frequency risk analysis)

  • Theoretical statistics for stochastic processes and limit theorems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2012.04
    -
    2016.03
     

    Yoshida Nakahiro, MASUDA Hiroki, MURATA Noboru, UCHIDA Masayuki, SHIMIZU Yasutaka, FUKASAWA Masaaki, KAMATANI Kengo

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    The quasi likelihood analysis was constructed for a stochastic regression model of volatility based on high frequency data in the finite time horizon, and an analytic criterion and a geometric criterion for non-degeneracy of the statistical random field associated with the quasi likelihood function were provided. The asymptotic mixed normality and the convergence of moments were proved. A quasi likelihood analysis was developed for a non-synchronously observed stochastic differential equation. Asymptotic expansion for a martingale with mixed normal limit was established. It is a new limit theorem beyond the frame of the present theory of asymptotic expansion for ergodic processes. The martingale expansion was applied to the p-variation. Studies of the asymptotic expansion of volatility estimators under microstructure noise have been developed. The spot volatility information criterion sVIC was proposed, and the fundamentals for developing computer software were studied.

  • Theoretical statistics for stochastic processes and limit theorems

    Project Year :

    2012.04
    -
    2015.03
     

     View Summary

    The quasi likelihood analysis was constructed for a stochastic regression model of volatility based on high frequency data in the finite time horizon, and an analytic criterion and a geometric criterion for non-degeneracy of the statistical random field associated with the quasi likelihood function were provided. The asymptotic mixed normality and the convergence of moments were proved. A quasi likelihood analysis was developed for a non-synchronously observed stochastic differential equation. Asymptotic expansion for a martingale with mixed normal limit was established. It is a new limit theorem beyond the frame of the present theory of asymptotic expansion for ergodic processes. The martingale expansion was applied to the p-variation. Studies of the asymptotic expansion of volatility estimators under microstructure noise have been developed. The spot volatility information criterion sVIC was proposed, and the fundamentals for developing computer software were studied

  • Stochastic Analysis and Statistical Inference for Insurance Ruin Risks

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2012.04
    -
    2015.03
     

    SHIMIZU Yasutaka

     View Summary

    As a generalization of the classical insurance ruin theory, we investigated a generalized Gerber-Shiu analysis under Levy insurance risk models. Main results are an extension of the ruin-related risk (Gerber-Shiu function) to a integral type functional of the insurance surplus, the derivation of its renewal type equation, and a representation theorem by a scale function for a spectrally negative Levy process. Moreover, we studied an inflation risk model written by a stochastic differential equation, and gave a bound of ruin probability and an optimal strategy of a reinsurance. In statistical analysis, we gave an approximation by the Edgeworth type expansion of ruin probability, inference for the Gerber-Shiu function from a discrete samples, and investigated the statistical error with the rate of convergence. We also show by simulations that these methodologies numerically work well

  • Theory and implementation of inference for semimartingales from discrete observations.

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2009
    -
    2011
     

    SHIMIZU Yasutaka

     View Summary

    We developed some statistical methodologies to estimate unknown parameters in stochastic models, which is used in financial and insurance applications. The estimators are based on a set of practical data, and has a mathematical validity. The implementation to a computational package is also ongoing

  • 統計サマーセミナー2009

    統計数理研究所  共同研究集会

    Project Year :

    2009.09
    -
     
     

    清水泰隆

  • Comprehensive study on statistical causal inference

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2006
    -
    2009
     

    KANO Yutaka, YANAGIMOTO Takemi, YAMAMOTO Eiji, SATO Toshiya, KUMAGAI Etsuo, YAMAGUCHI Kazunori, WATANABE Michiko, MIYAKAWA Masami, KUROKI Manabu, SHIGEMASU Kazuo, UENO Maomi, MOTOMURA Yoichi, TODAYAMA Kazuhisa, ICHINOSE Masaki, DEGUCHI Yasuo, ADACHI Kohei, KARASAWA Kaori, HAEBARA Tomokazu, INUI Toshio, SEIYAMA Kazuo, SHIMIZU Yasutaka, MIYAMOTO Yusuke, ICHIKAWA Masanori, YANAGIHARA Hirokazu, NAITO Kanta

     View Summary

    Active academic exchanges among researchers in statistical, informatics and social sciences, including philosophy of science in particular, have been made through hosting colloquiums of a few speakers regularly, symposiums of 10 to 15 talks several times a year, and international meetings. Some of our fruits obtained with the help of the governmental scientific research grant are i) a new robust methodology of the covariance selection, ii) a new method for determining direction of causation using nonnormality, ii) new estimation methods for data with nonignorable missing values in a 2 times 2 contingency table and a latent-variable model, and iii) clarification between conditional probability and scientific evidence

  • Development of practical inference for stochastic processes with jumps

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2007
    -
    2008
     

    SHIMIZU Yasutaka

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Specific Research

  • 死亡率予測モデルへの新アプローチと新たなスタンダードの確立

    2020  

     View Summary

    死亡率予測モデルとして全く新しいモデルを提案した.本研究では,死亡が起こる(根元的)原因をモデリングする.我々は人間に「生命エネルギー」なるものが存在すると仮定して,そのエネルギーの消滅によって死亡が起こると考え,その経時変化を確率過程によってモデリングすることで,死亡時刻の分布関数を陽に書き下すことにした.エネルギーモデルには,時間的に非一様な拡散過程を考え,そのゼロへの初期到達時刻の分布として,死亡時刻の分布族を提案した.モデルの良さはHuman Mortality Databaseを元に実証研究を行い,実際に長期予測に耐えられるモデルであることを実証した.この結果は国際誌ASTIN Bulletinに採択された.

  • 死亡率予測に対する確率解析的アプローチと統計的推測論

    2019  

     View Summary

    We proposed a quite new approach to the mortality prediction under the "Survival Energy Hypothesis (SEH)".We assume that a human is born with initial energy, which changes stochastically in time, and the human dies if the energy vanishes. Then, the time of death is represented by the first hitting time of the "survival energy (SE) processes" to zero. This paper assumes the SE follows a time-inhomogeneous diffusion process and define the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is actually very fictitious hypothesis, we illustrated that such an assumption had a potential to give a good parametric family of cumulative probability of death, and the parametric family could give surprisingly good prediction for distant future's mortality rate. 

  • アクチュアリアル・データ・サイエンスへの挑戦

    2018  

     View Summary

    保険会社の資産過程を連続時間の確率過程モデルを用いてモデリングし,ある境界への到達時刻の分布に対する期待値型汎関数を用いてリスクを把握し,このリスク量を資産データを用いて統計的に推測するための理論的基盤をつくる研究を行った.資産モデルが一定のレヴィ過程に従うという状況において,リスク量の確率解析的評価が可能になり,その特徴量をデータから統計的に推定することで,リスク量全体の推定を行った.時に高頻度な観測設定の下で,モデルにおける種々のパラメータ推定とその漸近的な一致性,漸近正規性などを数学的に証明し,これらを用いて,リスク量の信頼区間の構成や誤差評価などの統計的手法を与えた.

  • 保険数理における新しい動的リスク尺度の理論と応用

    2016  

     View Summary

    本研究では,保険の新しいソルベンシー基準に沿った,市場整合的なリスク評価のための新しいリスク尺度を提案した.この種の先行研究として破産確率をベースとしたリスク尺度の研究があるが,本研究では破産確率だけでなく,破産時の損害額や破産直前資産額など,実務的にも重要なリスク量を含めたリスク関数(Gerber-Shiu関数)の形で動的リスク尺度の一般化に成功した.この成果は保険数理に関する国際誌の特集号へ投稿中である.また,(c)の統計推測の理論と方法については,Gerber-Shiu関数のノンパラメトリック推定の枠組みで平均2乗の意味での一致性を持ち,最適収束率を達成する推定量の構成に成功した.これらは,保険数理の国際誌への掲載が決定している.

  • 保険リスク管理のための数学的・統計的リスク尺度の構築

    2015  

     View Summary

    本年の主要研究において,連続時間型のマルコフ過程を保険資産のモデルとして用い,そのプロセスの破産直前の値,破産時損害,破産時刻といった破産関連リスクに対する割引罰則関数(Gerber-Shiu関数)を一定水準以下に抑えるような備金によってリスクを評価するような新しいリスク尺度を定義し,それを資産過程がとるパス空間上におけるリスク尺度として数学的に良い性質を満たすことを証明.数学的正当化に成功した.これを基に,各時刻における条件付きバージョンが定義でき,破産リスクを経時的に評価できる新しいダイナミックリスク尺度を構築した.この成果は,日本大学の田中周二教授との共同研究として,保険数理関連の国際誌に投稿中である.

  • 保険数理における破産関連リスクの確率解析と統計科学の融合的研究

    2014   Runhuan Feng

     View Summary

    本研究では,損害保険数理に現れる保険ポートフォリオの破産問題の数学的一般化とその統計推測を主題として,(1) 資産モデルの一般化; (2) 一般化破産関連リスクの定式化と解析評価;(3)一般化破産リスクに対する統計推測理論の構築,に焦点を当てて研究を行った.これに対して,(1)では資産モデルを一般のレヴィ過程に拡張し,(2)ではGerber-Shiu関数を含むレヴィ過程の積分形汎関数を提案,その微分・積分方程式の導出に成功した.また(3)については,離散的な資産データによるノンパラメトリック推定量を提案し,そのL2誤差評価を与えた.

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Syllabus

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Committee Memberships

  • 2021.12
    -
    Now

    日本アクチュアリー会  評議員

  • 2019.03
    -
    Now

    日本アクチュアリー会  客員

  • 2018.04
    -
    Now

    Japanese Journal of Statistics and Data Science  編集委員

  • 2016.04
    -
    Now

    Journal of the Japanese Association of Risk, Insurance and Pensions  Editor

  • 2016.04
    -
    Now

    日本年金保険リスク学会誌  編集委員

  • 2014.04
    -
    Now

    Japan Journal of Industrial and Applied Mathematics  Associate Editor

  • 2016.10
    -
    2018.09

    日本数学会 社会連携協議会  幹事

  • 2013.04
    -
     

    日本数学会  統計数学分科会運営委員

  • 2007.04
    -
    2009.03

    日本統計学会  監事

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