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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.
In order to study the optimal investment with maintenance cost for a finite period of maturity, the relationship between the expected return of the company and the time and the company’s share capital is analyzed. Using the principle of dynamic programming and the knowledge of stochastic analysis, the company earnings function This mathematic model is a parabolic variational inequality with gradient constraint. By using the method of partial differential equation, the penalty function is constructed to prove the existence and uniqueness of the strong solution to this parabolic variational inequality and the corresponding The results show that the expected return of the company increases with the increase of the company’s share capital and decreases with the expiration of the expiration date.This has important theoretical value for guiding the enterprise to design the optimal investment strategy.