7 – Backward Stochastic Differential Equations
7 – Backward Stochastic Differential Equations
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DOI：
10.1533/9780857099402.235
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发表时间：
2011
影响因子：
0.3
通讯作者：
Xuerong Mao
中科院分区：
文献类型：
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作者：
Xuerong Mao
虽然鞅是随机积分的非线性扩展，但后向鞅是鞅表示定理的非线性版本。事实上，本章的结果和论证都与结合鞅表示定理的随机微分方程的结果和论证类似。给定2 L.F/，它自然地导出鞅Yt WD Et jFt。根据鞅表示定理，存在唯一的Z2L.F/，使得
While SDE is a nonlinear extension of the stochastic integration, Backward SDE is a nonlinear version of the martingale representation theorem. In fact, both the results and the arguments in this chapter are analogous to those for SDEs, combined with the martingale representation theorem. Given 2 L.F/, it induces naturally a martingale Yt WD EΠjFt . By the martingale representation theorem, there exists unique Z 2 L.F/ such that