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

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  • Jan Hendrik Witte
  • Christoph Reisinger

Abstract

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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  • Jan Hendrik Witte & Christoph Reisinger, 2011. "Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems," Papers 1105.5954, arXiv.org, revised Dec 2011.
    • Handle: RePEc:arx:papers:1105.5954
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    2. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, vol. 1(1), pages 75-107, December.
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