最优投资模型分析

Analysis of An Optimal Investment Model

为研究到期日是有限时间的带维修费的最优投资问题,分析了公司的期望收益与时间、公司的股本之间的关系:利用动态规划原理和随机分析的知识建立了公司收益函数所满足的数学模型,此数学模型是1个带梯度约束的抛物变分不等式;利用偏微分方程的方法,通过构造惩罚函数,证明了此抛物变分不等式强解的存在唯一性,并得到了相应的估计.结果表明,公司的期望收益随公司股本的增加而增加,随到期日的临近而递减.这对指导企业设计最优投资策略具有重要的理论价值.

The purpose of the paper is to study the optimal investment problem with maintenance expenditure of the firm with finite horizon,and to discuss the relationship between the firm＇s expected return and time and the firm＇s capital stock. Firstly,applying dynamic programming principle and stochastic analysis,the mathematical model of the company＇s revenue function is established,which satisfies a parabolic variational inequality with gradient constraint. Then,using the method of partial differential equation,the existence and uniqueness of strong solutions of the parabolic variational inequality are proved by constructing the penalty function,and the corresponding estimates are obtained. The results show that the expected return of the company increases with the increase of the company＇s capital stock,and decreases with the approaching of the expiration date. It has important theoretical value to guide the design of the optimal investment strategy.