Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications
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DOI：
10.1142/9789814324359_0019
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发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
S. Peng
中科院分区：
文献类型：
--
作者：
S. Peng
本文综述了近20年来倒向随机微分方程理论的发展，包括解的存在唯一性、比较定理、非线性Feynman-Kac公式、g-期望等许多重要结果，以及它们在不完全金融市场动态定价和套期保值中的应用。本文还提出了新的非线性期望框架及其在概率分布不确定性下的金融风险度量中的应用。在次线性期望下，大数定律的广义形式和中心极限定理表明极限分布是次线性的g正态分布。构造了一种新的布朗运动——g -布朗运动，它是在次线性期望（或非线性期望）下具有独立平稳增量的连续随机过程。
We give a survey of the developments in the theory of Backward Stochastic Differential Equations during the last 20 years, including the solutions’ existence and uniqueness, comparison theorem, nonlinear Feynman-Kac formula, g-expectation and many other important results in BSDE theory and their applications to dynamic pricing and hedging in an incomplete financial market. We also present our new framework of nonlinear expectation and its applications to financial risk measures under uncertainty of probability distributions. The generalized form of law of large numbers and central limit theorem under sublinear expectation shows that the limit distribution is a sublinear Gnormal distribution. A new type of Brownian motion, G-Brownian motion, is constructed which is a continuous stochastic process with independent and stationary increments under a sublinear expectation (or a nonlinear expectation).