Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates

详细信息    查看全文

• 作者：Xianggang Lu ; G. Yin ; Xianping Guo
• 关键词：Controlled diffusion ; Random and state ; dependent discount cost rate ; Hamilton–Jacobi–Bellman equation ; Verification theorem ; Numerical approximation
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：172
• 期：2
• 页码：535-553
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

This work focuses on optimal controls of diffusions in an infinite horizon. It has several distinct features in contrast to the existing literature. The discount factor is allowed to be randomly varying and state dependent. The existence and uniqueness of the viscosity solution to the associated Hamilton–Jacobi–Bellman equation are established. The verification theorem is also obtained. Because closed-form solutions are virtually impossible to obtain in most cases, we develop numerical methods. Using the Markov chain approximation methods, numerical schemes are constructed; viscosity solution methods are used to prove the convergence of the algorithm. In addition, examples are given for demonstration purpose.