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- Title
A numerical algorithm for fully nonlinear HJB equations: An approach by control randomization.
- Authors
Kharroubi, Idris; Langrené, Nicolas; Pham, Huyên
- Abstract
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [`Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE', Ann. Probab., to appear] for representing fully nonlinear HJB equations. This includes in particular numerical resolution for 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 algorithm error is presented, as well as numerical tests on the problem of option superreplication with uncertain volatilities and/or correlations, including a detailed comparison with the numerical results from the alternative scheme proposed in [J. Comput. Finance 14 (2011), 37-71].
- Subjects
STOCHASTIC differential equations; RANDOMIZATION (Statistics); DIFFERENTIAL equations; STOCHASTIC control theory; REGRESSION analysis; ALGORITHM research
- Publication
Monte Carlo Methods & Applications, 2014, Vol 20, Issue 2, p145
- ISSN
0929-9629
- Publication type
Article
- DOI
10.1515/mcma-2013-0024