具有特殊结构的多维二次和次二次BSDEs

Pub Date : 2013-09-26 DOI:10.1080/17442508.2015.1013959
Patrick Cheridito, Kihun Nam
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引用次数: 53

摘要

我们研究了具有有界末端条件和最多二次增长的驱动的多维BSDEs的形式。我们考虑三种不同的情况。在第一种情况下,BSDE是马尔可夫的,可以从相关FBSDE的解中得到解。在第二种情况下,当将BSDE投影到一维子空间时,BSDE变成了一维二次BSDE,并且可以从一维方程的解中得到解。在第三种情况下,驱动器的增长是严格次二次的,通过先在短时间区间上求解BSDE,然后递归扩展它,可以证明解的存在唯一性。
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Multidimensional quadratic and subquadratic BSDEs with special structure
We study multidimensional BSDEs of the formwith bounded terminal conditions and drivers that grow at most quadratically in . We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver in is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.
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