英文标题：
《A numerical algorithm for fully nonlinear HJB equations: an approach by
control randomization》
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作者：
Idris Kharroubi (CREST, CEREMADE), Nicolas Langren\\\'e (LPMA), Huy\\^en
Pham (CREST, LPMA)
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最新提交年份：
2013
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英文摘要：
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. 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].
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中文摘要：
我们提出了一种概率数值算法来求解具有非负跳的倒向随机微分方程（BSDE），这是[9]中介绍的一类BSDE，用于表示完全非线性的HJB方程。特别是，这使我们能够数值求解具有受控波动性（可能退化）的随机控制问题。我们基于最小二乘回归的反向方案利用了蒙特卡罗方法的高维特性，并以反馈形式为最优控制提供了参数估计。本文对方案的误差进行了部分分析，并对波动率和/或相关性不确定的期权的超复制问题进行了数值试验，包括与[7]中提出的替代方案的数值结果进行了详细比较。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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