Risk Analysis with Investment in Uncertain Environments

This paper focuses on the risk analysis of insurance company in uncertain environments. A risk model with an investment(IRM) is investigated, where the individual claim amount is assumed to be a fuzzy random variable and meanwhile the claim number process is characterized as a Poisson process. The mean chance of the ultimate ruin of the IRM is studied, particularly, its expression is given for the case of positive initial surplus and exponentially distributed fuzzy random individual claim amount. A portfolio model for solving the optimal investment strategy is provided and a monkey algorithm based on fuzzy simulation(FSMA) for obtaining the optimal proportion is designed. A numerical example shows that investment is an indispensable factor for the ultimate ruin of the insurance company.