一类非线性模型下的最优分红和风险控制策略

Optimal Dividend and Risk Control Strategies in a Nonlinear Model

本文用一类非线性模型模拟公司的资产过程,该模型反映了经营成本与业务规模之间的相关关系.假设公司可以通过调整业务规模、分红和融资控制资产过程,在控制过程中消耗比例交易费用和固定交易费用.在最大化公司价值的目标下,我们借助随机控制方法给出了最优的控制策略及值函数的显式解.结果显示,控制策略由模型参数共同决定,公司应当采用脉冲策略进行分红,资产增加时应扩大业务规模,当且仅当交易费用相对较小时选择脉冲策略进行融资以避免破产.

This paper assumes that company’s asset process follows a non-linear model,which reflects the relationship between the operation costs and the size business.Suppose that the company can control the asset process by changing the size of business,paying dividends and raising money dynamically.Meanwhile,it bears both fixed and proportional transaction costs during the control processes.Under the objective of maximizing the company’s value,we obtain the explicit solutions of optimal strategies and value function by using the optimal control method.The results illustrate that the optimal strategies depend on the parameters of the model.The company should expand the business scale with the increasing of asset.Dividends should be paid out according to the impulse control strategy.Financing is profitable to avoid bankruptcy if and only if the transaction costs are relatively low.