破产概率

PrefaceNotation and conventionsⅠ Introduction1 The risk process2 Claim size distributions3 The arrival process4 A summary of main results and methodsⅡ Martingales and simple ruin calculations1 Wald martingales2 Gambler's ruin.Two-sided ruin.Brownian motion3 Further simple martingale calculations4 More advanced martingalesⅢ Further general tools and results1 Likelihood ratios and change of measure2 Duality with other applied probability models3 Random walks in discrete or continuous time4 Markov additive processes5 The ladder height distributionⅣ The compound Poisson model1 Introduction2 The Pollaczeck-Khinchine formula3 Special cases of the Pollaczeck-Khinchine formula4 Change of measure via exponential families5 Lundberg conjugation6 Further topics related to the adjustment coefficient7 Various approximations for the ruin probability8 Comparing the risks of different claim size distributions9 Sensitivity estimates10 Estimation of the adjustment coefficientⅤ The probability of ruin within finite time1 Exponential claims2 The ruin probability with no initial reserve3 Laplace transforms4 When does ruin occur？5 Diffusion approximations6 Corrected diffusion approximations7 How does ruin occur？Ⅵ Renewal arrivals1 Introduction2 Exponential claims.The compound Poisson model with negative claims3 Change of measure via exponential families4 The duality with queueing theoryⅦ Risk theory in a Markovian environment1 Model and examples2 The ladder height distribution3 Change of measure via exponential families4 Comparisons with the compound Poisson model5 The Markovian arrival process6 Risk theory in a periodic environment7 Dual queueing modelsⅧ Level-dependent risk processes1 Introduction2 The model with constant interest3 The local adjustment coefficient.Logarithmic asymptotics4 The model with tax5 Discrete-time ruin problems with stochastic investment6 Continuous-time ruin problems with stochastic investmentⅨ Matrix-analytic methods1 Definition and basic properties of phase-type distributions2 Renewal theory3 The compound Poisson model4 The renewal model5 Markov-modulated input6 Matrix-exponential distributions7 Reserve-dependent premiums8 Erlangization for the finite horizon caseⅩ Ruin probabilities in the presence of heavy tails1 Subexponential distributions2 The compound Poisson model3 The renewal model4 Finite-horizon ruin probabilities5 Reserve-dependent premiums6 Tail estimationⅪ Ruin probabilities for Levy processes1 Preliminaries2 One-sided ruin theory3 The scale function and two-sided ruin problems4 Further topics5 The scale function for two-sided phase-type jumpsⅫ Gerber-Shiu functions1 Introduction2 The compound Poisson model3 The renewal model4 Levy risk modelsⅩⅢ Further models with dependence1 Large deviations2 Heavy-tailed risk models with dependent input3 Linear models4 Risk processes with shot-noise Cox intensities5 Causal dependency models6 Dependent Sparre Andersen models7 Gaussian models.Fractional Brownian motion8 Ordering ofruin probabilities9 Multi-dimensional risk processesⅩⅣ Stochastic control1 Introduction2 Stochastic dynamic programming3 The Hamilton-Jacobi-Bellman equationⅩⅤ Simulation methodology1 Generalities2 Simulation via the Pollaczeck-Khinchine formula3 Static importance sampling via Lundberg conjugation4 Static importance sampling for the finite horizon case5 Dynamic importance sampling6 Regenerative simulation7 Sensitivity analysisⅩⅥ Miscellaneous topics1 More on discrete-time risk models2 The distribution of the aggregate claims3 Principles for premium calculation4 ReinsuranceAppendixA1 Renewal theoryA2 Wiener-Hopf factorizationA3 Matrix-exponentialsA4 Some linear algebraA5 Complements on phase-type distributionsA6 Tauberian theoremsBibliographyIndex

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.