PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS—CONTINUOUS CONTROL AND OBSTACLE PROBLEMS

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 penalization error for a class of penalty terms, and we show that variations of Newton's method can be used to o...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 50; no. 2; pp. 595 - 625
Main Authors WITTE, J. H., REISINGER, C.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects
Algorithms
Applied mathematics
Approximation
Borrowing
Incomplete markets
Investors
Iterative solutions
Market prices
Markov analysis
Mathematical functions
Methods
Newtons method
Penalty function
Perceptron convergence procedure
Stochastic models
Viscosity
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Summary: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 penalization 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 penalized 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.
ISSN:0036-1429
1095-7170
DOI:10.1137/110835840