### Abstract

We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer's risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.

Original language | English |
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Pages (from-to) | 253-261 |

Number of pages | 9 |

Journal | Automatica |

Volume | 47 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2011 |

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## Cite this

*Automatica*,

*47*(2), 253-261. https://doi.org/10.1016/j.automatica.2010.10.032