具有状态转换的一般扩散模型中的最优融资和股利分配
Optimal financing and dividend distribution in a general diffusion model with regime switching
摘要：
本文研究了一类扩散型盈余模型中的最优融资和股利分配问题，其中漂移系数和波动系数是盈余水平和外部环境的一般函数。环境状况由马尔可夫过程建模。资本注入和股息支付都会产生费用。目标是最大化总贴现股息减去资本注入总成本的期望。我们证明了只有当盈余趋于下降到零以下时才注入资本是最优的，而当盈余处于或高于依赖于环境制度的阈值时才以最大的比率支付股息。
英文摘要：
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 injections and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of capital injections. We prove that it is optimal to inject capitals only when the surplus tends to fall below zero and to pay out dividends at the maximal rate when the surplus is at or above the threshold dependent on the environment regime.
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