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本文对扩散模型下的最优分红问题作了进一步分析.注意到,累积分红量是一个关于时间的右连左极过程,它的路径由连续和跳跃两部分组成.因此,本文在建模中同时加入了连续分红和脉冲分红两种形式,这就构成了一个正则和脉冲分红混合的最优控制问题.假设所有分红量存在一个比例成本,对于每次的脉冲分红量存在一个固定成本.此外,对于连续分红部分,假设存在一个有限的最大分红率.用漂移Brown运动描述公司的盈余过程,优化目标设定为最大化公司破产前分红现值的期望值,本文给出了值函数以及最优分红策略的解析表达式.结论表明,最优的分红策略为阀值(threshold)策略和脉冲策略的组合形式.
In this paper, we further analyze the optimal dividend problem under the diffusion model, and note that the cumulative dividend amount is a right-connected left-pole process about time, and its path consists of two parts: continuous and jump.Therefore, At the same time, the continuous dividend and pulse dividend are added simultaneously, which constitutes an optimal control problem for the mixture of regular and impulsive dividends. Assuming there is a proportional cost for all dividends, there is a fixed cost for each impulse dividend. , We assume that there exists a finite maximum dividend rate for the continuous dividend distribution. Using the Brownian motion to describe the company’s earnings process, the optimization goal is set as the expected value that maximizes the present value of the dividend before the bankruptcy. In this paper, we present the value function and the optimal The analytical expression of dividend strategy shows that the optimal dividend strategy is a combination of threshold strategy and impulsive strategy.