【作者】 刘郁菲；

【导师】 何春雄；

【作者基本信息】 华南理工大学 ， 概率论与数理统计， 2013， 硕士

【摘要】 在股份制公司中，公司治理的目标是制定一个分红策略，使股东收益在公司破产之前最大，也就是使未来红利的期望价值最大，该分红策略即为最优分红策略.本文研究了当公司的现金储备遵循双边跳跃扩散过程时的最优分红问题.假定公司的现金储备过程由三部分组成：带漂移的Brown运动，代表现金储备较小的变化；两个复合Poisson过程，分别代表现金储备向上和向下的较大的变化.公司面临两种流动性风险：Brown风险和Poisson风险.现金储备向上跳跃可以解释为公司的随机收益，例如，通过投资获得的初始资产；向下跳跃可以解释为公司的随机损失，例如，投资损失.本文中，首先介绍了分红策略的研究背景，并且还对研究内容和方法以及本文的结构进行了简要说明.另外，还介绍了本文所涉及到的基本概念和理论，主要有风险模型、效用理论、分红策略、随机过程和随机微分方程、随机控制理论.对于分红策略的研究，考虑了公司不能通过保险抵御Poisson风险时的情形，由随机控制理论推导出HJB方程，在障碍策略下构造出满足HJB方程的二阶连续可导的价值函数V，并证明价值函数V即为最优价值函数，最优分红策略是障碍策略：当现金储备小于临界值时，不支付红利；当现金储备大于临界值时，将超出临界值的部分作为红利支付给股东.我们还考虑了公司可以通过购买保险来抵御Poisson风险的情形，由随机控制理论给出了HJB方程，并且在障碍策略下构造了满足HJB方程的价值函数G.在给出保费金额和管理者要求的单位风险的预期收益率需要满足的条件下，证明了分红障碍唯一存在.最后，证明了在满足给定条件的情况下，价值函数G即为最优价值函数，最优分红策略仍为障碍策略，而且最优保险政策也是障碍策略：当现金储备高于临界值时购买保险，低于临界值时不买保险.更多还原

【Abstract】 In the joint-stock company, the purpose of corporate governance is setting a dividendpolicy to shareholders to maximize revenue before the company went bankrupt, or maximizethe expected value of future dividend, the dividend policy is the optimal. This paper studiesthe problem of optimal dividend when cash reserves of a company follow two-sidedjump-diffusion process. Assume that cash reserves process of a company consists of threeparts: the Brownian movement with drift that represents small movements in the cash flow;two compound Poisson processes that represent large movements in the cash flow up anddown. The company faces two types of liquidity risks: a Brownian risk and a Poisson risk.The upward jumps of the cash reserves can be interpreted as the random returns, for example,the initial assets by investment; the downward jumps can be interpreted as the random loss ofthe company, such as investment losses.In this paper, we first introduce the research background of dividend strategy, and make abrief description of the research content and methods, as well as the structure of this paper. Inaddition, we also introduce the basic concepts and theories related to this paper, mainlyinclude risk models, utility theory, dividend strategy, stochastic processes and stochasticdifferential equations, stochastic control theory.For the research of the dividend strategy, considering the situation that the companycouldn’t resist Poisson risk through insurance, we deduce the stochastic HJB equation by thestochastic control theory, construct a twice continuously differentiable value function Vsatisfying the HJB equation under the barrier strategy, and prove that the value function V isthe optimal value function, the optimal dividend policy is a barrier strategy: the firm keepscash inside when the cash reserves level is less than a critical threshold and pays cash inexcess of this threshold.We also consider the situation that the company can buy insurance to resist Poisson risk.We give the HJB equation by the stochastic control theory, and construct a value function Gsatisfying the HJB equation under the barrier strategy. Giving the conditions that the premiumamount and the expected return per unit of risk that the manager required need to meet, we prove the unique existence of dividend barrier. Lastly we prove that the value function G isthe optimal value function when the given conditions is satisfied, the optimal dividend policyis still a barrier strategy, and the optimal insurance policy is a barrier strategy: buy insurancewhen its cash reserves are above a critical threshold and not to insure otherwise.更多还原