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

被引：36

作者：

Kharroubi, Idris ^{[1
,2
]}

Langrene, Nicolas ^{[3
,4
]}

Huyen Pham ^{[3
,5
]}

机构：

[1] Univ Paris 09, CNRS UMR 7534, CEREMADE, Paris, France

[2] CREST, Paris, France

[3] Univ Paris Diderot, Lab Probabilites & Modeles Aleatoires, Paris, France

[4] EDF R&D, Palaiseau, France

[5] ENSAE, CREST, Toulouse, France

来源：

MONTE CARLO METHODS AND APPLICATIONS | 2014年 / 20卷 / 02期

关键词：

Backward stochastic differential equations; control randomization; HJB equation; uncertain volatility; empirical regressions; Monte Carlo;

D O I：

10.1515/mcma-2013-0024

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. 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 ofMonte 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 [7].

引用

页码：145 / 165

页数：21

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