Contents Preface Chapter 1 Introduction1 1.1 Risk process and ruin probabilities4 1.2 Claim size distributions and claim arrival process7 1.2.1 Claim size and heavy-tailed or light-tailed distributions7 1.2.2 The arrival process10 1.3 The Cramer-Lundberg Estimate12 Chapter 2 Risk Model with no Interest Rate17 2.1 Veraverbeke's theorem17 2.2 In-nite-time ruin probabilities in two dependent risk models 28 2.2.1 In-nite-time ruin probability with modulated claim sizes31 2.2.2 In-nite-time ruin probability with NUQD claim sizes 35 2.3 Finite-time ruin probabilities with NLQD inter-arrival times 36 2.4 Supremum of a dependent random walk with subexponential increments53 Chapter 3 Risk Model with Interest Rate66 3.1 Finite-time ruin probabilities with dominatedly-varying-tailed laim sizes67 3.1.1 Some existing results in the independence case67 3.1.2 Asymptotics and uniform asymptotics fornitetime ruin probabilities in thedependence case69 3.2 Further results on asymptotics and uniform asymptotics for ruin probabilitieswith dominatedly-varying-tailed claim sizes84 3.3 Finite-time ruin probabilities with subexponential claim sizes in the dependentcompound renewal risk model93 3.3.1 Compound renewal risk model and dependence structures93 3.3.2 Finite-time ruin probabilities with subexponential individual claim sizes97 3.3.3 Simulation study107 Chapter 4 Discrete-time Risk Model with Insurance andFinancial Risks111 4.1 Randomly weighted sums in the independence case112 4.1.1 Randomly weighted -nite sums112 4.1.2 Randomly weighted in-nite sums114 4.2 Randomly weighted sums in the dependence case115 4.2.1 Randomly weighted -nite sums with dependent primary random variables115 4.2.2 Randomly weighted -nite sums with dependence between the primary random variable and the random weight116 4.2.3 Randomly weighted in-nite sums with dependent primary random variables128 Bibliography141 编后记148
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