首页|Penalty and penalty-like methods for nonlinear HJB PDEs

Penalty and penalty-like methods for nonlinear HJB PDEs

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  • NSTL
  • Elsevier
There are numerous financial problems that can be posed as optimal control problems, leading to Hamilton-Jacobi-Bellman or Hamilton-Jacobi-Bellman-Issacs equations. We reformulate these problems as nonlinear PDEs, involving max and/or min terms of the unknown function, and/or its first and second spatial derivatives. We suggest efficient numerical methods for handling the nonlinearity in the PDE through an adaptation of the discrete penalty method Forsyth and Vetzal(2002)[1] that gives rise to tridiagonal penalty matrices. We formulate a penalty-like method for the use with European exercise rights, and extend this to American exercise rights resulting in a double-penalty method. We also use our findings to improve the policy iteration algorithms described in Forsyth and Labahn(2007)[2]. Numerical results are provided showing clear second-order convergence, and where applicable, we prove the convergence of our algorithms. (C) 2022 Published by Elsevier Inc.

Partial differential equationsBlack-ScholesNonlinear iterationFinite differencesCrank-NicolsonControl problemHamilton-Jacobi-Bellman (HJB) equationTransaction costsStock borrowing feesPenalty methodsCONVERGENCE PROPERTIESOPTIONSEQUATION

Christara, Christina C.、Wu, Ruining

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Univ Toronto

2022

10.1016/j.amc.2022.127015

Applied mathematics and computation

Applied mathematics and computation

EISCI
ISSN：0096-3003
年,卷(期)：2022.425
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