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破产概率 第2版 英文PDF|Epub|txt|kindle电子书版本网盘下载

破产概率 第2版 英文
  • （丹）阿斯姆森著 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：7510084490
  • 出版时间：2015
  • 标注页数：602页
  • 文件大小：71MB
  • 文件页数：619页
  • 主题词：概率论－研究－英文

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图书目录

Ⅰ Introduction1

1 The risk process1

2 Claim size distributions6

3 The arrival process11

4 A summary of main results and methods13

Ⅱ Martingales and simple ruin calculations21

1 Wald martingales21

2 Gambler's ruin.Two-sided ruin.Brownian motion23

3 Further simple martingale calculations29

4 More advanced martingales30

Ⅲ Further general tools and results39

1 Likelihood ratios and change of measure39

2 Duality with other applied probability models45

3 Random walks in discrete or continuous time48

4 Markov additive processes54

5 The ladder height distribution62

Ⅳ The compound Poisson model71

1 Introduction72

2 The Pollaczeck-Khinchine formula75

3 Special cases of the Pollaczeck-Khinchine formula77

4 Change of measure via exponential families82

5 Lundberg conjugation84

6 Further topics related to the adjustment coefficient91

7 Various approximations for the ruin probability95

8 Comparing the risks of different claim size distributions100

9 Sensitivity estimates103

10 Estimation ofthe adjustment coefficient110

Ⅴ The probability of ruin within finite time115

1 Exponential claims116

2 The ruin probability with no initial reserve121

3 Laplace transforms126

4 When does ruin occur?128

5 Diffusion approximations136

6 Corrected diffusion approximations139

7 How does ruin occur?146

Ⅵ Renewal arrivals151

1 Introduction151

2 Exponential claims.The compound Poisson model with negative claims154

3 Change of measure via exponential families157

4 The duality with queueing theory161

Ⅶ Risk theory in a Markovian environment165

1 Model and examples165

2 The ladder height distribution172

3 Change of measure via exponential families180

4 Comparisons with the compound Poisson model188

5 The Markovian arrival process194

6 Risk theory in a periodic environment196

7 Dual queueing models205

Ⅷ Level-dependent risk processes209

1 Introduction209

2 The model with constant interest222

3 The local adjustment coefficient.Logarithmic asymptotics227

4 The model with tax239

5 Discrete-time ruin problems with stochastic investment242

6 Continuous-time ruin problems with stochastic investment248

Ⅸ Matrix-analytic methods253

1 Definition and basic properties of phase-type distributions253

2 Renewal theory260

3 The compound Poisson model264

4 The renewal model266

5 Markov-modulated input271

6 Matrix-exponential distributions277

7 Reserve-dependent premiums281

8 Erlangization for the finite horizon case287

Ⅹ Ruin probabilities in the presence of heavy tails293

1 Subexponential distributions293

2 The compound Poisson model302

3 The renewal model305

4 Finite-horizon ruin probabilities309

5 Reserve-dependent premiums318

6 Tail estimation320

Ⅺ Ruin probabilities for Lévy processes329

1 Preliminaries329

2 One-sided ruin theory336

3 The scale function and two-sided ruin problems340

4 Further topics345

5 The scale function for two-sided phase-typejumps353

Ⅻ Gerber-Shiu functions357

1 Introduction357

2 The compound Poisson model360

3 The renewal model374

4 Lévy risk models384

ⅩⅢ Further models with dependence397

1 Large deviations398

2 Heavy-tailed risk models with dependent input410

3 Linear models417

4 Risk processes with shot-noise Cox intensities419

5 Causal dependency models424

6 Dependent Sparre Andersen models427

7 Gaussian models.Fractional Brownian motion428

8 Ordering of ruin probabilities433

9 Multi-dimensional risk processes435

ⅩⅣ Stochastic control445

1 Introduction445

2 Stochastic dynamic programming447

3 The Hamilton-Jacobi-Bellman equation448

ⅩⅤ Simulation methodology461

1 Generalities461

2 Simulation via the Pollaczeck-Khinchine formula465

3 Static importance sampling via Lundberg conjugation470

4 Static importance sampling for the finite horizon case474

5 Dynamic importance sampling475

6 Regenerative simulation482

7 Sensitivity analysis484

ⅩⅥ Miscellaneous topics487

1 More on discrete-time risk models487

2 The distribution of the aggregate claims493

3 Principles for premium calculation510

4 Reinsurance513

Appendix517

A1 Renewal theory517

A2 Wiener-Hopffactorization522

A3 Matrix-exponentials526

A4 Some linear algebra530

A5 Complements on phase-type distributions536

A6 Tauberian theorems548

Bibliography549

Index597

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