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Volume 15, Issue 3
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment

Jingtang Ma, Jie Xing & Shan Yang

DOI: 10.4208/nmtma.OA-2022-0001

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 641-661.

Published online: 2022-07

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  • 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.

  • Keywords

Optimal investment and consumption, stochastic control with optimal stopping, nonlinear free boundary problems, least-squares Monte-Carlo methods.

  • AMS Subject Headings

49M25, 91B70, 65C05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-641, author = {Ma , JingtangXing , Jie and Yang , Shan}, title = {Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0001}, url = {http://global-sci.org/intro/article_detail/nmtma/20810.html} }
TY - JOUR T1 - Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment AU - Ma , Jingtang AU - Xing , Jie AU - Yang , Shan JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 641 EP - 661 PY - 2022 DA - 2022/07 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2022-0001 UR - https://global-sci.org/intro/article_detail/nmtma/20810.html KW - Optimal investment and consumption, stochastic control with optimal stopping, nonlinear free boundary problems, least-squares Monte-Carlo methods. AB -

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.

Jingtang Ma, Jie Xing & Shan Yang. (2022). Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment. Numerical Mathematics: Theory, Methods and Applications. 15 (3). 641-661. doi:10.4208/nmtma.OA-2022-0001
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