A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
Pham, Huyên; Langrené, Nicolas; Kharroubi, Idris (2014), A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization, Monte Carlo Methods and Applications, 20, 2, p. 145–165. http://dx.doi.org/10.1515/mcma-2013-0024
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00905899
Journal nameMonte Carlo Methods and Applications
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Abstract (EN)We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in  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 .
Subjects / KeywordsMonte-Carlo; empirical regressions; uncertain volatility; HJB equation; control randomization; Backward stochastic differential equations
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