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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.

MSC:
91B28Finance etc. (MSC2000)
91B30Risk theory, insurance
60G44Martingales with continuous parameter
60H10Stochastic ordinary differential equations
60H30Applications of stochastic analysis