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 - <p style="text-align: justify;">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.</p>