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1.

図書
図書
1. Elementary stochastic calculus : with finance in view
Thomas Mikosch
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1998  ix, 212 p. ; 23 cm
シリーズ名: Advanced series on statistical science & applied probability ; v. 6
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2.

図書
図書
2. Modelling extremal events for insurance and finance. 4th corr. print. and 8th print (: alk. paper)
Paul Embrechts, Claudia Klüppelberg, Thomas Mikosch
出版情報: Berlin : Springer, 2008  xv, 648 p. ; 24 cm
シリーズ名: Stochastic modelling and applied probability ; 33
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3.

図書
図書
3. Modelling extremal events for insurance and finance
Paul Embrechts, Claudia Klüppelberg, Thomas Mikosch
出版情報: Berlin ; New York : Springer, c1997  xv, 645 p. ; 24 cm
シリーズ名: Applications of mathematics ; 33
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4.

図書
図書
4. Lévy processes : theory and applications (: Boston ; : Basel)
Ole E. Barndorff-Nielsen, Thomas Mikosch, Sidney I. Resnick, editors
出版情報: Boston : Birkhäuser, c2001  x, 415 p. ; 26 cm
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目次情報: 続きを見る
Preface
A tutorial on L+¼vy processes / Sato, KI：
Basic results on L+¼vy processes
Distributional, pathwise and structural results / Carmona, P ; Petit, F ; Yor, MII：
Exponentials functionals of Levy processes / Doney, R
Fluctuation theory for Levy processes / Marcus, M.B ; Rosen, J
Gaussian processes and the local times of symmetric L+¼vy processes / Watanabe, T
Temporal change in distributional properties of L+¼vy processes
Extensions and generalisations of L+¼vy processes / III：
Applebaum, D.: L+¼vy processes in stochastic differential geometry / Jac ; Schilling, R.L
L+¼vy-type processes and pseudo-differential operators / Maejima, M
Semi-stable distributions
Applications in physics / Albeverio, S ; R++diger, B ; Wu, J-LIV：
Analytic and probabilistic aspects of L+¼vy processes and fields in quantum theory / Holevo, A.S
L+¼vy processes and continuous quantum measurements / Woyczynski, W.A
L+¼vy processes in the physical sciences / Bertoin, J
Some properties of Burgers turbulence with white or stable noise
Applications in finance / Barndorff-Nielsen, O.E ; Shepard, NV：
Modelling by L+¼vy processes for financial econometrics / Eberlein, E
Application of generalized hyperbolic L+¼vy motions to finance / Ma, J ; Protter, P ; Zhang, J
Explicit form and path regularity of martingale representation
Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity
Numerical and statistical aspects / Nolan, J.PVI：
Maximum likelihood estimation and diagnostics for stable distributions / Rosinski, J
Series representations of L+¼vy processes from the perspective of point processes
Preface
A tutorial on L+¼vy processes / Sato, KI：
Basic results on L+¼vy processes
5.

図書
図書
5. Non-life insurance mathematics : an introduction with the Poisson process. 2nd ed
Thomas Mikosch
出版情報: Berlin : Springer, c2009  xv, 432 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Collective Risk Models / Part I：
The Basic Model / 1：
Models for the Claim Number Process / 2：
The Poisson Process / 2.1：
The Homogeneous Poisson Process, the Intensity Function, the Cramer-Lundberg Model / 2.1.1：
The Markov Property / 2.1.2：
Relations Between the Homogeneous and the Inhomogeneous Poisson Process / 2.1.3：
The Homogeneous Poisson Process as a Renewal Process / 2.1.4：
The Distribution of the Inter-Arrival Times / 2.1.5：
The Order Statistics Property / 2.1.6：
A Discussion of the Arrival Times of the Danish Fire Insurance Data 1980-1990 / 2.1.7：
An Informal Discussion of Transformed and Generalized Poisson Processes / 2.1.8：
Exercises
The Renewal Process / 2.2：
Basic Properties / 2.2.1：
An Informal Discussion of Renewal Theory / 2.2.2：
The Mixed Poisson Process / 2.3：
The Total Claim Amount / 3：
The Order of Magnitude of the Total Claim Amount / 3.1：
The Mean and the Variance in the Renewal Model / 3.1.1：
The Asymptotic Behavior in the Renewal Model / 3.1.2：
Classical Premium Calculation Principles / 3.1.3：
Claim Size Distributions / 3.2：
An Exploratory Statistical Analysis: QQ-Plots / 3.2.1：
A Preliminary Discussion of Heavy- and Light-Tailed Distributions / 3.2.2：
An Exploratory Statistical Analysis: Mean Excess Plots / 3.2.3：
Standard Claim Size Distributions and Their Properties / 3.2.4：
Regularly Varying Claim Sizes and Their Aggregation / 3.2.5：
Subexponential Distributions / 3.2.6：
The Distribution of the Total Claim Amount / 3.3：
Mixture Distributions / 3.3.1：
Space-Time Decomposition of a Compound Poisson Process / 3.3.2：
An Exact Numerical Procedure for Calculating the Total Claim Amount Distribution / 3.3.3：
Approximation to the Distribution of the Total Claim Amount Using the Central Limit Theorem / 3.3.4：
Approximation to the Distribution of the Total Claim Amount by Monte Carlo Techniques / 3.3.5：
Reinsurance Treaties / 3.4：
Ruin Theory / 4：
Risk Process, Ruin Probability and Net Profit Condition / 4.1：
Bounds for the Ruin Probability / 4.2：
Lundberg's Inequality / 4.2.1：
Exact Asymptotics for the Ruin Probability: the Small Claim Case / 4.2.2：
The Representation of the Ruin Probability as a Compound Geometric Probability / 4.2.3：
Exact Asymptotics for the Ruin Probability: the Large Claim Case / 4.2.4：
Experience Rating / Part II：
Bayes Estimation / 5：
The Heterogeneity Model / 5.1：
Bayes Estimation in the Heterogeneity Model / 5.2：
Linear Bayes Estimation / 6：
An Excursion to Minimum Linear Risk Estimation / 6.1：
The Buhlmann Model / 6.2：
Linear Bayes Estimation in the Buhlmann Model / 6.3：
The Buhlmann-Straub Model / 6.4：
A Point Process Approach to Collective Risk Theory / Part III：
The General Poisson Process / 7：
The Notion of a Point Process / 7.1：
Definition and First Examples / 7.1.1：
Distribution and Laplace Functional / 7.1.2：
Poisson Random Measures / 7.2：
Laplace Functional and Non-Negative Poisson Integrals / 7.2.1：
Properties of General Poisson Integrals / 7.2.3：
Construction of New Poisson Random Measures from Given Poisson Random Measures / 7.3：
Transformation of the Points of a Poisson Random Measure / 7.3.1：
Marked Poisson Random Measures / 7.3.2：
The Cramer-Lundberg and Related Models as Marked Poisson Random Measures / 7.3.3：
Aggregating Poisson Random Measures / 7.3.4：
Poisson Random Measures in Collective Risk Theory / 8：
Decomposition of the Time-Claim Size Space / 8.1：
Decomposition by Claim Size / 8.1.1：
Decomposition by Year of Occurrence / 8.1.2：
Decomposition by Year of Reporting / 8.1.3：
Effects of Dependence Between Delay in Reporting Time and Claim Size / 8.1.4：
Effects of Inflation and Interest / 8.1.5：
A General Model with Delay in Reporting and Settlement of Claim Payments / 8.2：
The Basic Model and the Basic Decomposition of Time-Claim Size Space / 8.2.1：
The Basic Decomposition of the Claim Number Process / 8.2.2：
The Basic Decomposition of the Total Claim Amount / 8.2.3：
An Excursion to Teletraffic and Long Memory: The Stationary IBNR Claim Number Process / 8.2.4：
A Critique of the Basic Model / 8.2.5：
Weak Convergence of Point Processes / 9：
Definition and Basic Examples / 9.1：
Convergence of the Finite-Dimensional Distributions / 9.1.1：
Convergence of Laplace Functionals / 9.1.2：
Point Processes of Exceedances and Extremes / 9.2：
Convergence of the Point Processes of Exceedances / 9.2.1：
Convergence in Distribution of Maxima and Order Statistics Under Affine Transformations / 9.2.2：
Maximum Domains of Attraction / 9.2.3：
The Point Process of Exceedances at the Times of a Renewal Process / 9.2.4：
Asymptotic Theory for the Reinsurance Treaties of Extreme Value Type / 9.3：
Special Topics / Part IV：
An Excursion to Levy Processes / 10：
Definition and First Examples of Levy Processes / 10.1：
Some Basic Properties of Levy Processes / 10.2：
Infinite Divisibility: The Levy-Khintchine Formula / 10.3：
The Levy-Ito Representation of a Levy Process / 10.4：
Some Special Levy Processes / 10.5：
Cluster Point Processes / 11：
The General Cluster Process / 11.1：
The Chain Ladder Method / 11.2：
The Chain Ladder Model / 11.2.1：
Mack's Model / 11.2.2：
Some Asymptotic Results in the Chain Ladder Model / 11.2.3：
Moments of the Chain Ladder Estimators / 11.2.4：
Prediction in Mack's Model / 11.2.5：
An Informal Discussion of a Cluster Model with Poisson Arrivals / 11.3：
Specification of the Model / 11.3.1：
An Analysis of the First and Second Moments / 11.3.2：
A Model when Clusters are Poisson Processes / 11.3.3：
References
Index
List of Abbreviations and Symbols
Collective Risk Models / Part I：
The Basic Model / 1：
Models for the Claim Number Process / 2：
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