Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process

Tatiana Belkina and Shangzhen Luo

North American Actuarial Journal, 2017, vol. 21, issue 1, 36-62

Abstract: 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.

Date: 2017
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DOI: 10.1080/10920277.2016.1246252

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