2015/02/08 by Belkina, Tatiana, Luo, Shangzhen
#49J22 #60G99 #91B28 #91B30 #93E20 #FOS: Economics and business #Portfolio Management (q-fin.PM)
paper · doi:10.48550/arxiv.1502.02286
We study an optimal investment control problem for an insurance company. The surplus process follows the Cramer-Lundberg process with perturbation of a Brownian motion. The company can invest its surplus into a risk free asset and a Black-Scholes risky asset. The optimization objective is to minimize the probability of ruin. We show by new operators that the minimal ruin probability function is a classical solution to the corresponding HJB equation. Asymptotic behaviors of the optimal investment control policy and the minimal ruin probability function are studied for low surplus levels with a general claim size distribution. Some new asymptotic results for large surplus levels in the case with exponential claim distributions are obtained. We consider two cases of investment control - unconstrained investment and investment with a limited amount.