Optimal investment for an insurer: the martingale approach. (English) Zbl 1141.91470

Summary: We apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer. When the insurer’s risk process is modeled by a Lévy process and the capital can be invested in a security market described by the standard Black-Scholes model, closed-form solutions to the problems of mean-variance efficient investment and expected CARA utility maximization are obtained. The effect of the claim process on the mean-variance efficient strategies and frontier is also analyzed.


91G10 Portfolio theory
91B30 Risk theory, insurance (MSC2010)
60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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