项目名称: 机制转化下的最优停时问题研究---以金融中投资决策分析为例
项目编号: No.11426115
项目类型: 专项基金项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 闫中凤
作者单位: 暨南大学
项目金额: 3万元
中文摘要: 本项目从理论证明和数值计算两方面来探讨机制转换下的最优停时问题,该问题的研究背景为金融学中的投资决策分析。研究内容包括:(1)建立两类可以刻画不同投资环境的机制转换模型:①具有反馈效应的机制转换模型。②转移密度矩阵为时间依赖的机制转换模型。(2)运用变分不等式的理论来分析该停时问题解的存在性、唯一性。并研究自由边界的单调性、光滑性以及自由边界的位置。(3)选用高效的数值算法,如随机逼近、差分法等得到该问题的数值解。本项目的研究将不仅丰富金融投资理论、随机控制理论,同时也能应用于能源开发、生物数学等领域。
中文关键词: 机制转换;最优投资;博弈理论;变分不等式;
英文摘要: This proposal is going to investigate the optimal stopping problem with regime switching theoretically and numerically, which arises in the investment of financial economics. The main research topics include:(1) We intend to set up regime switching models which can better reveal the behavior of the economic conditions, such as regime switching model with feedback effect and time varying transition probability matrix. (2)By employing the variational inequality theory, we will study the existence and uniqueness of the solution of the problem as well as the properties and the location of the free boundary. (3)In addition, numerical studies (stochastic approximation, difference method) will be performed to gain some insights of the solution.Our framework can be applied not only in financial engineering, control and optimization but also in manufacturing system and Biological Mathematics.
英文关键词: regime switching;optimal investment;game theory;variational inquality;