Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment
Year: 2022
Author: Jie Xing, Jingtang Ma, Shan Yang, Jie Xing, Shan Yang
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 641–661
Abstract
This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation (CEV) model with finite horizon. Two risky assets are involved in the model with one following geometric Brownian motion and the other a CEV model. This problem is a kind of two dimensional mixed control and optimal stopping problems with finite horizon. The existence and continuity of the optimal retirement threshold surfaces are proved and the working and retirement regions are characterized theoretically. Least-squares Monte-Carlo methods are developed to solve this mixed control and optimal stopping problem. The algorithms are well implemented and the optimal retirement threshold surfaces, optimal investment strategies and the optimal consumptions are drawn via examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0001
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 641–661
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Optimal investment and consumption stochastic control with optimal stopping nonlinear free boundary problems least-squares Monte-Carlo methods.