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An optimal investment strategy in a Markov-modulated risk model: maximizing the terminal utility. (English) Zbl 1289.91098
Summary: The surplus of an insurance company is governed by a jump-diffusion process, and it can be invested in a financial market with one risk-free asset and $$N$$ risky assets. The parameters of the surplus process and the asset price processes depend on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. To maximize the terminal utility, we focus on finding an optimal investment strategy and solve it by using the HJB equation. An explicit expression for the optimal strategy and the corresponding objective function are presented when the company has an exponential utility function. Some interesting economic interpretations are involved.
##### MSC:
 91B30 Risk theory, insurance (MSC2010) 91G10 Portfolio theory 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B16 Utility theory