Research On The Ruin Probability In Two Types Of Risk Model

In this paper,we discuss infinite time ruin probabilities in a compound Poisson processthat is perturbed by diffusion with constant interest force and in a compound binomialrisk model with constant interest rates or random interest rates.First of all,we consider the classical risk model disturbed by diffusion with constantinterest force. The renewal equation for the probability of survival is derived by differen-tial approach,and asymptotic formular for the infinite time ruin probability are given byrenewal theory.Differential equation satisfied by the survival probability is derived whenthe claim sizes are exponential.Upper bound is obtained by Laplace transform.Second, we consider the compound binomial risk model under constant interestrate.Upper bounds for the infinite time ruin probability is obtained by inductive andmartingale approaches.We give a numerical example to illustrate the bounds.Third,we consider the compound binomial risk model under random interest rates.Upper bounds for the infinite time ruin probability is obtained by inductive and martingaleapproaches.We give a numerical example to illustrate the bounds.