Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order
Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order
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DOI：
10.1007/978-1-4612-2022-0_2
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
É. Pardoux
中科院分区：
文献类型：
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作者：
É. Pardoux
本文的目的是提出倒向随机微分方程（简称倒向随机微分方程）的理论，以及它与抛物型和椭圆型半线性二阶偏微分方程（简称倒向随机微分方程）的粘性解的联系。线性BSDEs很早以前就出现了，它既是随机控制中伴随过程的方程，也是数学金融中Black和Scholes期权定价和套期保值公式背后的模型。这些线性bsde可以或多或少地显式求解（参见定理1.4的证明）。
The aim of this article is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semilinear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs appeared long time ago, both as the equations for the adjoint process in stochastic control, as well as the model behind the Black and Scholes formula for the pricing and hedging of options in mathematical finance. These linear BSDEs can be solved more or less explicitly (see proof of Theorem 1.4).