Asymptotic Investment Behaviors Under A Jump-Diffusion Risk Process
North American Actuarial Journal
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.
Department of Mathematics
Original Publication Date
DOI of published version
UNI ScholarWorks, Rod Library, University of Northern Iowa
Belkina, Tatiana and Luo, Shangzhen, "Asymptotic Investment Behaviors Under A Jump-Diffusion Risk Process" (2017). Faculty Publications. 932.