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arXiv · 1502.02286

Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process

Tatiana Belkina·Shangzhen Luo
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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.

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Tatiana Belkina, Shangzhen Luo. 2015-02-08. Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process. https://arxiv.org/abs/1502.02286

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