Generalized Poisson Models and Their Applications in Insurance and Finance

, by Bening, Vladimir E.; Korolev, Victor Yu

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9789067643665 | 9067643661
Cover: Hardcover
Copyright: 7/1/2002

Rent

(Recommended)

$328.04

Term

Due

Price

Semester

Dec 12

$345.31

Quarter

Aug 13

$328.04

Short Term

Jul 20

$310.78

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Special Order: 1-2 Weeks

$442.08
eBook

Available Instantly

Online: 1825 Days

Downloadable: Lifetime Access

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$536.40*

Contents include: Basic notions of probability theory. Poisson Process. Convergence of superpositions of independent stochastic processes. Compound Poisson distributions. Classical risk processes. Doubly stochastic Poisson processes (Cox processes). Compound Cox processes with zero mean. Modeling evolution of stock prices by compound Cox processes. Compound Cox processes with non-zero mean. Functional limit theorems for compound Cox processes. Generalized risk processes. Statistical inference concerning the parameters of risk processes. Bibliography.

Foreword

Preface

xiii

Basic notions of probability theory

(68)

Random variables, their distributions and moments

(10)

Generating and characteristic functions

(10)

Random vectors. Stochastic independence

(3)

Weak convergence of random variables and distribution functions

(6)

Poisson theorem

(5)

Law of large numbers. Central limit theorem. Stable laws

(10)

The Berry--Esseen inequality

(2)

Asymptotic expansions in the central limit theorem

(9)

Elementary properties of random sums

(6)

Stochastic processes

(7)

Poisson process

(14)

The definition and elementary properties of a Poisson process

(3)

Poisson process as a model of chaotic displacement of points in time

(2)

The asymptotic normality of a Poisson process

(2)

Elementary rarefaction of renewal processes

(7)

Convergence of superpositions of independent stochastic processes

(40)

Characteristic features of the problem

(2)

Approximation of distributions of randomly indexed random sequences by special mixtures

(4)

The transfer theorem. Relations between the limit laws for random sequences with random and non-random indices

(2)

Necessary and sufficient conditions for the convergence of distributions of random sequences with independent random indices

(7)

Convergence of distributions of randomly indexed sequences to identifiable location or scale mixtures. The asymptotic behavior of extremal random sums

(7)

Convergence of distributions of random sums. The central limit theorem and the law of large numbers for random sums

105

(10)

A general theorem on the asymptotic behavior of superpositions of independent stochastic processes

115

(2)

The transfer theorem for random sums of independent identically distributed random variables in the double array limit scheme

117

(6)

Compound Poisson distributions

123

(58)

Mixed and compound Poisson distributions

123

(6)

Discrete compound Poisson distributions

129

(4)

The asymptotic normality of compound Poisson distributions. The Berry--Esseen inequality for Poisson random sums. Non-central Lyapunov fractions

133

(6)

Asymptotic expansions for compound Poisson distributions

139

(12)

The asymptotic expansions for the quantiles of compound Poisson distributions

151

(4)

Exponential inequalities for the probabilities of large deviations of Poisson random sums. An analog of Bernshtein--Kolmogorov inequality

155

(2)

The application of Esscher transforms to the approximation of the tails of compound Poisson distributions

157

(9)

Estimates of convergence rate in local limit theorems for Poisson random sums

166

(15)

Classical risk processes

181

(52)

The definition of the classical risk process. Its asymptotic normality

181

(4)

The Pollaczek-Khinchin--Beekman formula for the ruin probability in the classical risk process

185

(4)

Approximations for the ruin probability with small safety loading

189

(2)

Asymptotic expansions for the ruin probability with small safety loading

191

(12)

Approximations for the ruin probability

203

(10)

Asymptotic approximations for the distribution of the surplus in general risk processes

213

(8)

A problem of inventory control

221

(6)

A non-classical problem of optimization of the initial capital

227

(6)

Doubly stochastic Poisson processes (Cox processes)

233

(32)

The asymptotic behavior of random sums of random indicators

233

(5)

Mixed Poisson processes

238

(11)

The modified Pollaczek--Khinchin--Beekman formula

249

(3)

The definition and elementary properties of doubly stochastic Poisson processes

252

(4)

The asymptotic behavior of Cox processes

256

(9)

Compound Cox processes with zero mean

265

(26)

Definition. Examples

265

(1)

Conditions of convergence of the distributions of compound Cox processes with zero mean. Limit laws

266

(3)

Convergence rate estimates

269

(4)

Asymptotic expansions for the distributions of compound Cox processes with zero mean

273

(8)

Asymptotic expansions for the quantiles of compound Cox processes with zero mean

281

(2)

Exponential inequalities for the probabilities of large deviations of compound Cox processes with zero mean

283

(2)

Limit theorems for extrema of compound Cox processes with zero mean

285

(2)

Estimates of the rate of convergence of extrema of compound Cox processes with zero mean

287

(4)

Modeling evolution of stock prices by compound Cox processes

291

(26)

Introduction

291

(1)

Normal and stable models

292

(2)

Heterogeneity of operational time and normal mixtures

294

(3)

Inhomogeneous discrete chaos and Cox processes

297

(6)

Restriction of the class of mixing distributions

303

(4)

Heavy-tailedness of scale mixtures of normals

307

(1)

The case of elementary increments with non-zero means

308

(2)

Models within the double array limit scheme

310

(3)

Quantiles of the distributions of stock prices

313

(4)

Compound Cox processes with nonzero mean

317

(40)

Definition. Examples

317

(1)

Conditions of convergence of compound Cox processes with nonzero mean. Limit laws

318

(4)

Convergence rate estimates for compound Cox processes with nonzero mean

322

(4)

Asymptotic expansions for the distributions of compound Cox processes with nonzero mean

326

(12)

Asymptotic expansions for the quantiles of compound Cox processes with nonzero mean

338

(1)

Exponential inequalities for the negative values of the surplus in collective risk models with stochastic intensity of insurance payments

339

(3)

Limit theorems for extrema of compound Cox processes with nonzero mean

342

(5)

Convergence rate estimates for extrema of compound Cox processes with nonzero mean

347

(3)

Minimum admissible reserve of an insurance company with stochastic intensity of insurance payments

350

(1)

Optimization of the initial capital of an insurance company in a static insurance model with random portfolio size

351

(6)

Functional limit theorems for compound Cox processes

357

(16)

Functional limit theorems for non-centered compound Cox processes

357

(6)

Functional limit theorems for nonrandomly centered compound Cox processes

363

(10)

Generalized risk processes

373

(18)

The definition of generalized risk processes

373

(2)

Conditions of convergence of the distributions of generalized risk processes

375

(3)

Convergence rate estimates for generalized risk processes

378

(3)

Asymptotic expansions for the distributions of generalized risk processes

381

(3)

Asymptotic expansions for the quantiles of generalized risk processes

384

(2)

Exponential inequalities for the probabilities of negative values of generalized risk processes

386

(5)

Statistical inference concerning the parameters of risk processes

391

(24)

Statistical estimation of the ruin probability in classical risk processes

391

(4)

Specific features of statistical estimation of ruin probability for generalized risk processes

395

(3)

A nonparametric estimator of the ruin probability for a generalized risk process

398

(6)

Interval estimator of the ruin probability for a generalized risk process

404

(8)

Computational aspects of the construction of confidence intervals for the ruin probability in generalized risk processes

412

(3)

Bibliography

415

(16)

Index

431

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Generalized Poisson Models and Their Applications in Insurance and Finance

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Generalized Poisson Models and Their Applications in Insurance and Finance

Summary

Table of Contents

Supplemental Materials

Digital License