Study On Ruin Probability Of Several Risk Models

Insurance risk theory is one of the most important research fields in the field of financial mathematics,and it is also one of the most active research directions in actuarial science.It has important theoretical significance for the risk management of insurance companies.The main contents of this paper are as follows:Firstly,a new model is considered with an investment portfolio under constant interest and inflation,where the arrival of term policies is generalized to Poisson process.In order to make the model follow with reality,the model contained multiple-type insurance and surrender.In this model,the claim processes followed a p-thinner process and surrender process followed a thinner process of the arrival of policies process.The formula of ultimate ruin probability of this model and an equation of ruin probability were given by the method of martingale.Secondly,surrender is included in jump-diffusion risk model with risk investment.In order to decline the risk,proportion reinsurance is bought by insurer.Under the rule of maximizing the exponent expected utility function,optimal investment strategy and optimal reinsurance ratio were found,and what were proved is that investment is better than no investment and optimal reinsurance ratio is influenced by risk investment.In the end,relevant conclusions were shown by numerical simulation.Thirdly,the classic discrete risk model is generalized.Insurer used the time difference from the initial premium charged to final claims for a short-term risk investment in each period.In the model risk assets were buy at the beginning of the period and sold at the final.The expression of ruin probability and the ruin probability Lundberg upper bound for the new model were calculated,and the effect of the risk investment on the adjustment coefficient and premium volume is illustrated.At last,an improved potential claim risk model is proposed,in which the fixed premium is replaced by a random variable with multiple values and the claim sequence’s independence is replaced by extended negatively dependence.Under the assumption that the claim amount distribution belongs to class L(40)D,an asymptotical expression of the finite-time ruin probability is derived.