破产概率 第二版（英文版）
作者：（丹）阿斯姆森 著
出版时间：2015年版
内容简介
This book is a second edition of the book of the same title by the first authorwhich was published in 2000. The subject of ruin probabilities and related top- ics has since then undergone a considerable development, not to say boom. This much expanded and revised second edition aims at covering a substantial part of these developments as well as the classical topics.
R,isk theory in general and ruin probabilities in particular are traditionally considered as part of insurance mathematics, and has been an active area of research from the days of Lundberg all the way up to today. One reason for writing tlus book is a feeling that the area has in recent years achieved a con-siderable mathematical maturity, which has in particular removed one of the standard criticisms of the area, namely that it can only say something about very simple models and questions. Although in insurance practice, usually sim- pler (and coarser) risk measures like Value-at-Risk are used, it is widely believed that the thinking advocated by ruin theory is still important for modern risk management. For instance, in times of market-consistent valuation principles, the role of the time diversification effect of insurance portfolios, which is one of the core elements of ruin theory, should not be forgotten. In addition, ruin the- ory has fruitful methodological links and applications to other fields of applied probability, like queueing theory and mathematical finance (pricing of barrier options, credit products etc.). Apart from these remarks, we have deliberately stayed away from discussing the practical relevance of the theory; if the formu- lations occasionally give a different impression, it is not by intention. Thus, the book is basically mathematical in its flavor.
目录
Preface
Notation and conventions
Ⅰ Introduction
1 The risk process
2 Claim size distributions
3 The arrival process
4 A summary of main results and methods
Ⅱ Martingales and simple ruin calculations
1 Wald martingales
2 Gambler's ruin.Two-sided ruin.Brownian motion
3 Further simple martingale calculations
4 More advanced martingales
Ⅲ Further general tools and results
1 Likelihood ratios and change of measure
2 Duality with other applied probability models
3 Random walks in discrete or continuous time
4 Markov additive processes
5 The ladder height distribution
Ⅳ The compound Poisson model
1 Introduction
2 The Pollaczeck-Khinchine formula
3 Special cases of the Pollaczeck-Khinchine formula
4 Change of measure via exponential families
5 Lundberg conjugation
6 Further topics related to the adjustment coefficient
7 Various approximations for the ruin probability
8 Comparing the risks of different claim size distributions
9 Sensitivity estimates
10 Estimation of the adjustment coefficient
Ⅴ The probability of ruin within finite time
1 Exponential claims
2 The ruin probability with no initial reserve
3 Laplace transforms
4 When does ruin occur？
5 Diffusion approximations
6 Corrected diffusion approximations
7 How does ruin occur？
Ⅵ Renewal arrivals
1 Introduction
2 Exponential claims.The compound Poisson model with negative claims
3 Change of measure via exponential families
4 The duality with queueing theory
Ⅶ Risk theory in a Markovian environment
1 Model and examples
2 The ladder height distribution
3 Change of measure via exponential families
4 Comparisons with the compound Poisson model
5 The Markovian arrival process
6 Risk theory in a periodic environment
7 Dual queueing models
Ⅷ Level-dependent risk processes
1 Introduction
2 The model with constant interest
3 The local adjustment coefficient.Logarithmic asymptotics
4 The model with tax
5 Discrete-time ruin problems with stochastic investment
6 Continuous-time ruin problems with stochastic investment
Ⅸ Matrix-analytic methods
1 Definition and basic properties of phase-type distributions
2 Renewal theory
3 The compound Poisson model
4 The renewal model
5 Markov-modulated input
6 Matrix-exponential distributions
7 Reserve-dependent premiums
8 Erlangization for the finite horizon case
Ⅹ Ruin probabilities in the presence of heavy tails
1 Subexponential distributions
2 The compound Poisson model
3 The renewal model
4 Finite-horizon ruin probabilities
5 Reserve-dependent premiums
6 Tail estimation
Ⅺ Ruin probabilities for Levy processes
1 Preliminaries
2 One-sided ruin theory
3 The scale function and two-sided ruin problems
4 Further topics
5 The scale function for two-sided phase-type jumps
Ⅻ Gerber-Shiu functions
1 Introduction
2 The compound Poisson model
3 The renewal model
4 Levy risk models
ⅩⅢ Further models with dependence
1 Large deviations
2 Heavy-tailed risk models with dependent input
3 Linear models
4 Risk processes with shot-noise Cox intensities
5 Causal dependency models
6 Dependent Sparre Andersen models
7 Gaussian models.Fractional Brownian motion
8 Ordering ofruin probabilities
9 Multi-dimensional risk processes
ⅩⅣ Stochastic control
1 Introduction
2 Stochastic dynamic programming
3 The Hamilton-Jacobi-Bellman equation
ⅩⅤ Simulation methodology
1 Generalities
2 Simulation via the Pollaczeck-Khinchine formula
3 Static importance sampling via Lundberg conjugation
4 Static importance sampling for the finite horizon case
5 Dynamic importance sampling
6 Regenerative simulation
7 Sensitivity analysis
ⅩⅥ Miscellaneous topics
1 More on discrete-time risk models
2 The distribution of the aggregate claims
3 Principles for premium calculation
4 Reinsurance
Appendix
A1 Renewal theory
A2 Wiener-Hopf factorization
A3 Matrix-exponentials
A4 Some linear algebra
A5 Complements on phase-type distributions
A6 Tauberian theorems
Bibliography
Index
