My Wish Lists Login / Join

Universitext

An Introduction with the Poisson Process

By: Thomas Mikosch

Write A Review

Paperback | 25 March 2009 | Edition Number 2

At a Glance

Paperback
450 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 15.24 x 1.91

Paperback

$129.00

or 4 interest-free payments of $32.25 with

Ships in 5 to 7 business days

The second edition of this book contains both basic and more advanced - terial on non-life insurance mathematics. Parts I and II of the book cover the basic course of the 1rst edition; this text has changed very little. It aims at the undergraduate (bachelor) actuarial student as a 1rst introduction to the topics of non-life insurance mathematics. Parts III and IV are new. They can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate (master) level. The basic themes in all parts of this book are point process theory, the Poisson and compound Poisson processes. Point processes constitute an - portant part of modern stochastic process theory. They are well understood models and have applications in a wide range of applied probability areas such as stochastic geometry, extreme value theory, queuing and large computer networks, insurance and finance. The main idea behind a point process is counting. Counting is bread and butter in non-life insurance: the modeling of claim numbers is one of the - jor tasks of the actuary. Part I of this book extensively deals with counting processes on the real line, such as the Poisson, renewal and mixed Poisson processes. These processes can be studied in the point process framework as well, but such an approach requires more advanced theoretical tools.

Industry Reviews

From the reviews:

"The book offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties. ... The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy. Special emphasis is given to the phenomena which are caused by large claims in these models." (Zentralblatt fuer Didaktik der Mathematik, November, 2004)

"The author's aim to bring some of the standard stochastic models of non-life insurance mathematics to the attention of a wide audience ... can definitely be reached by this textbook. It is well-written ... . Many figures and tables in this book help in illustrating and visualizing the developed theory. Moreover, every section ends with an extensive collection of exercises... and should help the reader in accessing the theory." (Josef Steinebach, Zentralblatt MATH, Vol. 1033 (8), 2004)

From the reviews of the second edition:

"The brief summary of the book's contents and purpose ... describes it as a mathematical introduction to non-life insurance, and it introduces the appropriate range of stochastic processes for this purpose. ... The book is based upon lectures given to 3^rd year mathematics students ... . this book is suited to study at the advanced undergraduate level at the earliest. Overall, this is a fascinating book on a subject ... ." (P. N. Ruane, The Mathematical Association of America, August, 2009)

"The book contains both basic and more advanced material on non-life insurance mathematics. ... aim at the undergraduate actuarical students. ... can serve as an independent course on stochastic models of non-life insurance mathematics at the graduate level." (Alexandra Rodkina, Zentralblatt MATH, Vol. 1166, 2009)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Accounting & Finance Finance Insurance & Actuarial Studies Mathematics Applied Mathematics

Collective Risk Models
The Basic Model	p. 3
Models for the Claim Number Process	p. 7
The Poisson Process	p. 7
The Homogeneous Poisson Process, the Intensity Function, the Cramer-Lundberg Model	p. 9
The Markov Property	p. 12
Relations Between the Homogeneous and the Inhomogeneous Poisson Process	p. 14
The Homogeneous Poisson Process as a Renewal Process	p. 16
The Distribution of the Inter-Arrival Times	p. 20
The Order Statistics Property	p. 22
A Discussion of the Arrival Times of the Danish Fire Insurance Data 1980-1990	p. 32
An Informal Discussion of Transformed and Generalized Poisson Processes	p. 35
Exercises	p. 46
The Renewal Process	p. 53
Basic Properties	p. 53
An Informal Discussion of Renewal Theory	p. 60
Exercises	p. 65
The Mixed Poisson Process	p. 66
Exercises	p. 69
The Total Claim Amount	p. 71
The Order of Magnitude of the Total Claim Amount	p. 72
The Mean and the Variance in the Renewal Model	p. 73
The Asymptotic Behavior in the Renewal Model	p. 74
Classical Premium Calculation Principles	p. 78
Exercises	p. 80
Claim Size Distributions	p. 82
An Exploratory Statistical Analysis: QQ-Plots	p. 82
A Preliminary Discussion of Heavy- and Light-Tailed Distributions	p. 86
An Exploratory Statistical Analysis: Mean Excess Plots	p. 88
Standard Claim Size Distributions and Their Properties	p. 94
Regularly Varying Claim Sizes and Their Aggregation	p. 99
Subexponential Distributions	p. 103
Exercises	p. 106
The Distribution of the Total Claim Amount	p. 109
Mixture Distributions	p. 110
Space-Time Decomposition of a Compound Poisson Process	p. 115
An Exact Numerical Procedure for Calculating the Total Claim Amount Distribution	p. 120
Approximation to the Distribution of the Total Claim Amount Using the Central Limit Theorem	p. 125
Approximation to the Distribution of the Total Claim Amount by Monte Carlo Techniques	p. 130
Exercises	p. 138
Reinsurance Treaties	p. 142
Exercises	p. 149
Ruin Theory	p. 151
Risk Process, Ruin Probability and Net Profit Condition	p. 151
Exercises	p. 156
Bounds for the Ruin Probability	p. 157
Lundberg's Inequality	p. 157
Exact Asymptotics for the Ruin Probability: the Small Claim Case	p. 162
The Representation of the Ruin Probability as a Compound Geometric Probability	p. 172
Exact Asymptotics for the Ruin Probability: the Large Claim Case	p. 174
Exercises	p. 177
Experience Rating
Bayes Estimation	p. 187
The Heterogeneity Model	p. 187
Bayes Estimation in the Heterogeneity Model	p. 189
Exercises	p. 195
Linear Bayes Estimation	p. 199
An Excursion to Minimum Linear Risk Estimation	p. 200
The Buhlmann Model	p. 204
Linear Bayes Estimation in the Buhlmann Model	p. 206
The Buhlmann-Straub Model	p. 209
Exercises	p. 211
A Point Process Approach to Collective Risk Theory
The General Poisson Process	p. 215
The Notion of a Point Process	p. 215
Definition and First Examples	p. 215
Distribution and Laplace Functional	p. 222
Exercises	p. 224
Poisson Random Measures	p. 226
Definition and First Examples	p. 227
Laplace Functional and Non-Negative Poisson Integrals	p. 232
Properties of General Poisson Integrals	p. 236
Exercises	p. 242
Construction of New Poisson Random Measures from Given Poisson Random Measures	p. 244
Transformation of the Points of a Poisson Random Measure	p. 244
Marked Poisson Random Measures	p. 246
The Cramer-Lundberg and Related Models as Marked Poisson Random Measures	p. 249
Aggregating Poisson Random Measures	p. 254
Exercises	p. 256
Poisson Random Measures in Collective Risk Theory	p. 259
Decomposition of the Time-Claim Size Space	p. 259
Decomposition by Claim Size	p. 259
Decomposition by Year of Occurrence	p. 261
Decomposition by Year of Reporting	p. 263
Effects of Dependence Between Delay in Reporting Time and Claim Size	p. 264
Effects of Inflation and Interest	p. 266
Exercises	p. 267
A General Model with Delay in Reporting and Settlement of Claim Payments	p. 268
The Basic Model and the Basic Decomposition of Time-Claim Size Space	p. 268
The Basic Decomposition of the Claim Number Process	p. 271
The Basic Decomposition of the Total Claim Amount	p. 273
An Excursion to Teletraffic and Long Memory: The Stationary IBNR Claim Number Process	p. 278
A Critique of the Basic Model	p. 284
Exercises	p. 286
Weak Convergence of Point Processes	p. 291
Definition and Basic Examples	p. 292
Convergence of the Finite-Dimensional Distributions	p. 292
Convergence of Laplace Functionals	p. 294
Exercises	p. 299
Point Processes of Exceedances and Extremes	p. 300
Convergence of the Point Processes of Exceedances	p. 300
Convergence in Distribution of Maxima and Order Statistics Under Affine Transformations	p. 305
Maximum Domains of Attraction	p. 309
The Point Process of Exceedances at the Times of a Renewal Process	p. 316
Exercises	p. 321
Asymptotic Theory for the Reinsurance Treaties of Extreme Value Type	p. 324
Exercises	p. 331
Special Topics
An Excursion to Levy Processes	p. 335
Definition and First Examples of Levy Processes	p. 335
Exercises	p. 338
Some Basic Properties of Levy Processes	p. 338
Exercises	p. 340
Infinite Divisibility: The Levy-Khintchine Formula	p. 341
Exercises	p. 347
The Levy-Ito Representation of a Levy Process	p. 348
Exercises	p. 355
Some Special Levy Processes	p. 355
Exercises	p. 361
Cluster Point Processes	p. 363
The General Cluster Process	p. 363
The Chain Ladder Method	p. 365
The Chain Ladder Model	p. 365
Mack's Model	p. 366
Some Asymptotic Results in the Chain Ladder Model	p. 369
Moments of the Chain Ladder Estimators	p. 372
Prediction in Mack's Model	p. 376
Exercises	p. 381
An Informal Discussion of a Cluster Model with Poisson Arrivals	p. 386
Specification of the Model	p. 386
An Analysis of the First and Second Moments	p. 389
A Model when Clusters are Poisson Processes	p. 394
Exercises	p. 402
References	p. 405
Index	p. 413
List of Abbreviations and Symbols	p. 429
Table of Contents provided by Ingram. All Rights Reserved.

Universitext

An Introduction with the Poisson Process

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Economics, Finance, Business and Management

The Simple Guide to ADHD Regulation

The Secret to Finding Balance, Getting Things Done, and Enjoying Your Life

John Longmire

Pain, perspective and premierships - my autobiography

Unreasonable Hospitality

The Remarkable Power of Giving People More Than They Expect

How the World Works

Built to Burn

Why Work Burns People Out and How the Best Leaders Build Cultures That Don't

101 Ways to Save Money on Your Tax - Legally! 2026 - 2027

The Quick-Start Guide to Your First Property

Pick Up Your Keys Simpler, Smarter and Sooner

It''s a Rich Man''s World

Why Money is Broken and How We Fix It, from the founders of Female Invest

Poor Charlie's Almanack

The Essential Wit and Wisdom of Charles T. Munger

From the Ground Up

How to build a cult brand

Mission Ready

SAS Commander's Strategies for Resilience, Leadership and Elite Performance

Abundance

THE INSTANT NEW YORK TIMES BESTSELLER and SHORTLISTED FOR THE FT BUSINESS BOOK AWARD: How We Build a Better Future

The Common Good Economy

A New Compass

Getting Murdoched

How Murdochâs Media Wields Power and Punishment

Innovation in Action

Unlock Curiosity, Creativity and Clarity with the DUCTRI Toolkit

Coaching Habit

Say Less, Ask More & Change the Way You Lead Forever

The Little Book of Common Sense Investing

The Only Way to Guarantee Your Fair Share of Stock Market Returns

She's on the Money

Take Charge of Your Financial Future

Contemporary Issues in Accounting

3rd Edition

Cultural Safety in Trauma-Informed Practice from a First Nations Perspective

Billabongs of Knowledge

From Strength to Strength

Finding Success, Happiness and Deep Purpose in the Second Half of Life

Questions Every Seller Must Ask

How to Avoid Costly Mistakes and Sell Your Home for More

Full Stack Human

The Mindset Upgrade You Need to Stay Human in a World Ruled by Technology

The Kind Way

The Life-Changing Metric for Leadership, Success and the Human Spirit

This product is categorised by