Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs.

*(English)*Zbl 1156.91395Summary: We consider the optimal financing and dividend control problem of the insurance company with fixed and proportional transaction costs. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance process to maximize the expected present value of the dividends payout minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model with two kinds of transaction costs, which come from real financial market has been considered. We solve the mixed classical-impulse control problem by constructing two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

91G10 | Portfolio theory |

91B16 | Utility theory |

60H05 | Stochastic integrals |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

##### Keywords:

optimal dividend control; optimal financing control; proportional reinsurance; HJB equation; fixed transaction cost; classical-impulse control
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\textit{L. He} and \textit{Z. Liang}, Insur. Math. Econ. 44, No. 1, 88--94 (2009; Zbl 1156.91395)

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