A numerical algorithm for fully nonlinear HJB equations: An approach by control randomization
A numerical algorithm for fully nonlinear HJB equations: An approach by control randomization
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DOI：
10.1515/mcma-2013-0024
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发表时间：
2014-06-01
影响因子：
0.9
通讯作者：
Huyen Pham
中科院分区：
文献类型：
--
作者：
Kharroubi, Idris;Langrene, Nicolas;Huyen Pham
我们提出了一种概率数值算法来求解具有非负跳跃的后向随机微分方程（BSDE），这是[9]中引入的一类 BSDE，用于表示完全非线性 HJB 方程。这尤其包括具有受控波动性（可能是退化）的随机控制问题的数值分辨率。我们的后向方案基于最小二乘回归，利用蒙特卡罗方法的高维特性，并且还以反馈形式提供参数估计以用于最优控制。提出了算法误差的部分分析，以及对具有不确定波动性和/或相关性的期权超级复制问题的数值测试，包括与[7]中提出的替代方案的数值结果的详细比较。
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].