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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:

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.) |

### Keywords:

mean-variance efficient portfolio; martingale approach; forward-backward stochastic differential equation (FBSDE); insurer
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\textit{Z. Wang} et al., Insur. Math. Econ. 40, No. 2, 322--334 (2007; Zbl 1141.91470)

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### References:

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