Ruin Probability For Risk Model In Stochastic Economic Environment

In the present actuarial science and mathematics research, risk theory is a hot topic. At first people make use of stochastic processes to study compound Poisson risk models, discuss the ruin probability and deficit at ruin and surplus immediately before ruin and the time of ruin and the joint distribution of other actuarial diagnostics. As the scale of the business expand incessantly and environment of business changes, people begin to generalize the classical risk models. This thesis discusses generalized compound Poisson risk models.In chapter 1 we briefly review the risk theory and its development and my innovations. In chapter 2 we discuss also discuss a compound Poisson surplus process is invested in a stochastic return which is assumed to be a Brownian motion with random variable. We derive (expected discounted) penalty function associated with the time of ruin of integral equation and applying penalty function we can obtain the other quantities. In chapter 3 this model allows for stochastic rate of return on investments as well as stochastic level of inflation. We construct the martingale to obtain the probability of eventual survival. In chapter 4 error in a known result about formula of ruin probability is corrected. In chapter 5 we briefly reviewed the whole paper and put forward the further tasks.