BMAP模型中最优分红和注资问题

Optimal Dividend and Capital Injection Problem in a BMAP Model

研究了BMAP(Batch Markov Arrival Process)模型中有分红和资金注入的情况下,公司的最优分红和注资问题.假设公司的盈余过程中的参数由BMAP模型中的相过程调制.在不同的跳跃点上,该公司有不同的分红和注资机会:在BMAP的一些跳跃点上,公司既没有分红也没有注资;在BMAP的一些跳跃点上,公司只有分红没有注资;在BMAP的另外一些跳跃点上,公司既有分红又有注资.通过将BMAP模型转化为辅助马氏调制模型的方法,在公司不破产的情况下,考虑公司的最优分红和注资问题,旨在使期望折现分红总量与折现注资量之差达到最大,得到了值函数的精确解以及最优分红-注资策略.

This paper studies the optimal dividend and capital injection problem of a company in a BMAP （Batch Markov Arrival Process） model. The parameters in the process of the company＇s surplus are modulated by the phase process of the BMAP, which is an observable continuous-time Markov chain. The possible dividend and capital injection are restricted to some random discrete time points which are determined by the same BMAP. The company has both dividend and capital injection opportunities or only has dividend but not capital injection opportu- nities at some of these time points, while can do nothing at other random time points. By transforming the BMAP model to an auxiliary Markov modulated model, we study the optimal dividend and capital injection problem of the company under the assumption that the company will not bankrupt. This paper aims to maximize the difference between the total expected discounted dividend and the amount of capital and obtain the exact solution of the value functions and the optimal dividend and capital injection strategy.