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Volume 17, Issue 2
Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping

Jingtang Ma, Jianjun Ma & Haofei Wu

DOI: 10.4208/nmtma.OA-2023-0094

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 404-428.

Published online: 2024-05

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  • Abstract

The aim of this paper is to solve the Hamilton-Jacobi-Bellman (HJB) quasi-variational inequalities arising in regime switching utility maximization with optimal stopping. The HJB quasi-variational inequalities are penalized into the HJB equations and the convergence of the viscosity solution of the penalized HJB equations to that of the HJB variational inequalities is proved. The finite difference methods with iteration policy are used to solve the penalized HJB equations and the convergence is proved. The approach is implemented via numerical examples and the figures for the exercise boundaries and optimal strategies with sample paths are sketched.

  • Keywords

Utility maximization, optimal stopping, stochastic control, regime switching, HJB variational inequalities, finite difference methods, iteration policy.

  • AMS Subject Headings

65C20, 65C40, 65M06, 91G20, 91G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-404, author = {Ma , JingtangMa , Jianjun and Wu , Haofei}, title = {Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {2}, pages = {404--428}, abstract = {

The aim of this paper is to solve the Hamilton-Jacobi-Bellman (HJB) quasi-variational inequalities arising in regime switching utility maximization with optimal stopping. The HJB quasi-variational inequalities are penalized into the HJB equations and the convergence of the viscosity solution of the penalized HJB equations to that of the HJB variational inequalities is proved. The finite difference methods with iteration policy are used to solve the penalized HJB equations and the convergence is proved. The approach is implemented via numerical examples and the figures for the exercise boundaries and optimal strategies with sample paths are sketched.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0094}, url = {http://global-sci.org/intro/article_detail/nmtma/23106.html} }
TY - JOUR T1 - Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping AU - Ma , Jingtang AU - Ma , Jianjun AU - Wu , Haofei JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 404 EP - 428 PY - 2024 DA - 2024/05 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0094 UR - https://global-sci.org/intro/article_detail/nmtma/23106.html KW - Utility maximization, optimal stopping, stochastic control, regime switching, HJB variational inequalities, finite difference methods, iteration policy. AB -

The aim of this paper is to solve the Hamilton-Jacobi-Bellman (HJB) quasi-variational inequalities arising in regime switching utility maximization with optimal stopping. The HJB quasi-variational inequalities are penalized into the HJB equations and the convergence of the viscosity solution of the penalized HJB equations to that of the HJB variational inequalities is proved. The finite difference methods with iteration policy are used to solve the penalized HJB equations and the convergence is proved. The approach is implemented via numerical examples and the figures for the exercise boundaries and optimal strategies with sample paths are sketched.

Jingtang Ma, Jianjun Ma & Haofei Wu. (2024). Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping. Numerical Mathematics: Theory, Methods and Applications. 17 (2). 404-428. doi:10.4208/nmtma.OA-2023-0094
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