Risk analysis of double-type-insurance with investment in uncertain environments

This paper focuses on the problem of risk analysis when investment is considered for an insurer in an uncertain environment, where the individual claim amount is assumed as a fuzzy random variable and the claim number processes are characterized as Poisson processes. To minimize the mean chance of ultimate ruin, a double-type-insurance risk model with an investment (DIRM) is built, particularly, the expression of the mean ruin chance of the DIRM is given for the case of zero and positive initial surplus and exponentially distributed fuzzy random individual claim amount. A numerical example solved by a monkey algorithm based on fuzzy simulation (FSMA) shows that investment is an indispensable factor for the ultimate ruin of the insurance companies.