Risk Analysis Of Insurance

In the context of Insurance Actuarial Mathematics, risk theory has received considerable attention on actuarial theory and its applications recently. The impact of fluctuation of interest rate and premium rate on insurance agent is outstanding. As the trade of the business risk, insurance agent's own risk can't be ignored. Proceeding from this reality, this paper studies deeply ruin problem of risk models under interest rate and premium rate. The aim is offering help in theory for insurance company to evade risk and work better.This paper sets up several models on constant interest rate, random interest rate and random premium rate.These models develop the current models in the literature and are more close to the reality. By researching models, the integral equation for the ruin probability is obtained. The lower and upper bounds for the ultimate ruin probability and the properties for the distribution functions of other ruin quantities are given.At first, we introduce the present position of risk theory. The basic theories about interest, martingale approach and stochastic processes are provided.Next, Erlang(n) risk model under constant interest rate is discussed. In the model, integral equation for the non-ruin probability and upper bounds for the ruin probability are obtained, the properties for the distribution functions of two ruin quantities which are the surplus immediately before ruin, the deficit at ruin are derived, so is their joint distribution.The expected value of a discounted function of the surplus immediately prior to ruin and the defict at ruin when ruin occurs is considered.By making use of the results, the model with n = 2 is discussed. These are generalizations of the current model and conclusion.At last risk model with random premium and stochastic interest rate is researched respectively. In the Erlang(2) model with random premium, according to the strong Markov property of surplus process at the moments of claims, the integral equation for ruin probability is derived. Finally the Lundberg upper bounds for ruin probability are obtained. In the delayed renewal risk model, asymptotic expression for finite time ruin probability is obtained and the result is extended to Equilibrium renewal process.In the latter, integral equation and estimate for the ruin probability of the Erlang(n) risk model with random interest rate are given.These results advance the current conclusions in the literature.