## Abstract

We study the optimal financing and dividend distribution problem with restricted dividend

rates in a diffusion type surplus model, where the drift and volatility coefficients are

general functions of the level of surplus and the external environment regime. The

environment regime is modeled by a Markov process. Both capital injection and dividend

payments incur expenses. The objective is to maximize the expectation of the total

discounted dividends minus the total cost of the capital injection. We prove that it is

optimal to inject capital only when the surplus tends to fall below 0 and to pay out

dividends at the maximal rate when the surplus is at or above the threshold, dependent

on the environment regime.

rates in a diffusion type surplus model, where the drift and volatility coefficients are

general functions of the level of surplus and the external environment regime. The

environment regime is modeled by a Markov process. Both capital injection and dividend

payments incur expenses. The objective is to maximize the expectation of the total

discounted dividends minus the total cost of the capital injection. We prove that it is

optimal to inject capital only when the surplus tends to fall below 0 and to pay out

dividends at the maximal rate when the surplus is at or above the threshold, dependent

on the environment regime.

Original language | English |
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Pages (from-to) | 406-422 |

Journal | Advances in Applied Probability |

Volume | 48 |

Issue number | 2 |

Publication status | Published - 2016 |

Externally published | Yes |