Ruin Probability And Numerical Simulation Of Discrete Time Risk Model

In this thesis, we firstly introduce the relevant knowledge of the classical risk model, renewal theory and method of martingale. Secondly, in the case of premium income and the amount claim is a random variable, we study the ruin probability of discrete time risk model with Markov interest rate and interest rate of MA (1). Using the methods of recursive and martingale, the theoretical solutions of upper bound of ruin probability are derived and numerical simulation shows upper bounds for inductive and martingale are better than Lundberg. Finally, under the tail distribution of net loss (difference of the premium and the amount claim) which belongs to different heavy-tailed distributions, we consider the ruin probability. Numerical simulation is used to obtain the lower bound of the pros and cons. The full thesis is divided into five parts as follows:The first chapter is introduction, we introduce the domestic and international research development on the risk theory, the background and meaning of the research.In second chapter, we introduce the classical risk theory and some prior knowledge which will be used in this thesis.In third chapter, we study the ruin probabilities of risk models with Markov interest rates, the integral equations and upper bound expressions of the ruin probabilities are given. Numerical simulation shows that upper bound for inductive and martingale are better than Lundberg.In fourth chapter, Ruin probability in MA(1) stochastic interest rate model is mainly studied, we consider the interest rates is MA(1) model, the integral equations and upper bound expressions of the ruin probabilities are given. Numerical simulation results show that the research generalizes the corresponding result of the classical risk model.In fifth chapter, under the tail distribution of distribution function which is belongs to several types of heavy-tailed distributions, we study the ruin probability. The classes of ERV and (?)∩(?) are selected to discuss the ruin probabilities, we give the upper and lower bounds, numerical simulation for ruin probabilities are given at last.