Asymptotic Investment Behaviors under a Jump-Diffusion Risk Process |
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Authors: | Tatiana Belkina |
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Institution: | 1. Laboratory of Stochastic Optimization and Risk Theory, Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia;2. International Laboratory of Quantitative Finance, National Research University Higher School of Economics, Moscow, Russia |
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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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