Non-life insurance mathematics : an introduction with the Poisson process

>> Google Books

所蔵情報QRコード

Non-life insurance mathematics : an introduction with the Poisson process / Thomas Mikosch

版:: 2nd ed
資料種別:: 図書
出版情報:: Berlin : Springer, c2009
形態:: xv, 432 p. ; 24 cm
シリーズ名:: Universitext <BA00021004>
著者名:: Mikosch, Thomas <DA1070974X>
ISBN:: 9783540882329 [3540882324]
書誌ID:: BA89676488

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. [405]-412) and index

主題:

Insurance--Mathematics; Stochastic processes

言語:

英語

目次情報:

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：

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：

続きを見る

東工大ブックレビュー

類似資料:

1 図書 Modelling extremal events for insurance and finance (: alk. paper) Embrechts, Paul, 1953-, Klüppelberg, Claudia, 1953-, Mikosch, Thomas Springer	7 図書 Stochastic processes for insurance and finance Rolski, Tomasz J. Wiley
2 図書 Modelling extremal events for insurance and finance Embrechts, Paul, 1953-, Klüppelberg, Claudia, 1953-, Mikosch, Thomas Springer	8 図書 Stochastic storage processes : queues, insurance risk, dams, and data communication (: hardcover) Prabhu, N. U. (Narahari Umanath), 1924- Springer
3 図書 Actuarial mathematics for life contingent risks (: hbk) Dickson, David C. M., 1959-, Hardy, Mary, Waters, H. R. (Howard Richard) Cambridge University Press	9 図書 An introduction to actuarial studies (: hbk.) Atkinson, M. E. (Margaret E.), 1952-, Dickson, David C. M., 1959- Edward Elgar
4 図書 Poisson and jump-point processes Ephremides, Anthony Dowden, Hutchinson & Ross	10 図書 Mathematical methods in risk theory Bühlmann, Hans Springer
5 電子ブック Lectures on the Poisson Process / ((ebook)) Last, Günter, Penrose, Mathew	11 図書 Fundamentals of actuarial mathematics Promislow, S. David John Wiley
6 図書 Practical risk theory for actuaries Daykin, C. D. (Chris D.), Pentikäinen, Teivo, Pesonen, M. (Martti) Chapman & Hall	12 図書 Introduction to stochastic processes Çınlar, Erhan, 1941- Prentice-Hall