On approximating the minimum initial capital of fire insurance with the finite-time ruin probability using a simulation approach

Abstract

This paper considers the discrete time surplus process in the case of fire insurance given by U_0=u,U_n=U_(n-1)+cZ_n-Y_n, where {Y_n,n≥1} is the claim severity process, {Z_n,n≥1} is the inter-arrival process, c is the premium rate, and U_0=u≥0 is the initial capital. The claim severities and the inter-arrival time are provided by the Thai Reinsurance Public Co., Ltd. In addition, we assume that {Y_n,n≥1} and {Z_n,n≥1} are independent and identically distributed, Y_n has Weibull distribution and Z_n has Poisson distribution. By using the maximum likelihood estimator method, we find that〖 Y〗_n~Weibull(0.8484,30.5396) and   Z_n~Poisson(37.8958). Finally, we approximate the finite-time ruin probability for one year by a simulation approach, and use the logarithmic regression to approximate the minimum initial capital corresponding to the quantities of risk α=0.01 and 0.05, respectively.