破产概率-第2版_PDF下载[100MB-百度云]阿斯姆森

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这是一部学习概率和应用概率推荐的书籍，将经典破坏概率和现代破坏概率巧妙结合，全面处理了应用概率的已知结果。考虑到涉及的专题有：Lundberg不等式；Cramer-Lundberg逼近；准确解；其他逼近；有限时间的破坏概率；经典复合Poisson模型等。在新的版本里做了大量扩充和更新，新的科目话题包括随机控制、Levy过程的起伏理论、Gerber Shiu函数和独立。

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PrefaceNotation and conventionsI Introduction 1 The risk process 2 Claim size distributions 3 The arrival process 4 A summary of main results and methodsII 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 martingalesIII 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 distributionIV The compound Poisson model 1 Introduction 2 The Pollaczeck-Khinchine formula 3 Spe 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 coefficientV 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 theoryVII 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 modelsVIII 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 investmentIX 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 caseX 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 estimationXI 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 jumpsXII Gerber-Shiu functions 1 Introduction 2 The compound Poisson model 3 The renewal model 4 Levy risk modelsXIII 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 of ruin probabilities 9 Multi-dimensional risk processesXIV Stochastic control 1 Introduction 2 Stochastic dynamic programming 3 The Hamilton-Jacobi-Bellman equationXV 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 analysisXVI Miscellaneous topics 1 More on discrete-time risk models 2 The distribution of the aggregate claims 3 Principles for premium calculation 4 ReinsuranceAppendix A1 Renewal theory A2 Wiener-Hopf factorization A3 Matrix-exponentials A4 Some linear algebra A5 Complements on phase-type distributions A6 Tauberian theoremsBibliographyIndex