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Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process

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  • Tatiana Belkina
  • Shangzhen Luo

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.

Suggested Citation

  • Tatiana Belkina & Shangzhen Luo, 2015. "Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process," Papers 1502.02286, arXiv.org.
    • Handle: RePEc:arx:papers:1502.02286
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    Cited by:

    1. Landriault, David & Li, Bin & Loke, Sooie-Hoe & Willmot, Gordon E. & Xu, Di, 2017. "A note on the convexity of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 1-6.

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