Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems

Details Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems

2011-05-30

arxiv.org/abs/1105.5954v2

SIAM J. Numer. Anal. 50(2), 595-625, 2012

Economy

Quantitative Finance

Computational Finance

31 Pages, 7 Figures

Scientific paper

10.1137/110835840

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalised equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods.

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