A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization

Idris Kharroubi, Nicolas Langren\'e and Huy\^en Pham
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Idris Kharroubi: CREST, CEREMADE
Nicolas Langren\'e: LPMA
Huy\^en Pham: CREST, LPMA

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Abstract: We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility, possibly degenerate. Our backward scheme, based on least-squares regressions, takes advantage of high-dimensional properties of Monte-Carlo methods, and also provides a parametric estimate in feedback form for the optimal control. A partial analysis of the error of the scheme is provided, as well as numerical tests on the problem of superreplication of option with uncertain volatilities and/or correlations, including a detailed comparison with the numerical results from the alternative scheme proposed in [7].

Date: 2013-11
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Published in Monte Carlo Methods and Applications 20(2) 145-165 (2014)

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