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

Xianggang Lu (), G. Yin () and Xianping Guo ()
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Xianggang Lu: Sun Yat-Sen University
G. Yin: Wayne State University
Xianping Guo: Sun Yat-Sen University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 2, No 10, 535-553

Abstract: Abstract 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.

Keywords: Controlled diffusion; Random and state-dependent discount cost rate; Hamilton–Jacobi–Bellman equation; Verification theorem; Numerical approximation; 93E20; 91G80; 60J60 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0898-x

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