Ruin Probabilities For General Insurance Models Involving Investments

In this paper we study the ruin problem for insurance models that involve investments. this paper's risk reserve process is an extension of the classical Cramer-Lundberg model,which will contain stochastic interest rates,reserve-dependent expense loading,diffusion perturbed models,jump process,and many other special cases.By introducing a new type of exponential martingale parameterizcd by a general rate function,we put various Crame r-Lundberg type estimations into a unified framework.This paper is organized as follows: The first chapter introduces related research at home and abroad,this paper's main methods and it's significance in economic;The second chapter gives risk reserve process and jump-diffuse financial market models,introduces stochastic point process theory and the definition of ruin probability;The third chapter constructs a type of exponential martingale parameterized by a general rate function and gives proof of related proposition of martingale;The fourth chapter mainly introduces how to deduce the Lundberg bound by the exponential martingale and gives two theorems;The fifth chapter simulates ruin probability and compare it with it's Lundberg bound to find out the distance between them,the results show that the Lundberg bound deduced by mathematical methods is little large.