Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators
Multi-Dimensional Backward Stochastic Differential Equations of Diagonally Quadratic generators
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DOI：
10.1016/j.spa.2015.10.011
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发表时间：
2014-08
期刊：
影响因子：
--
通讯作者：
Ying Hu;Shanjian Tang
中科院分区：
文献类型：
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作者：
Ying Hu;Shanjian Tang
本文研究了一个具有对角二次生成元的多维Bronze，其第i个分量的二次部分只依赖于第二个未知变量的第i行。局部和整体的解决方案，这似乎是第一个系统的（积极的）结果的一般可解性的多维二次倒向随机微分方程。在我们的证明中，对BMO鞅同时应用John-Nirenberg不等式和逆Hölder不等式是很自然和重要的。最后，我们的结果被证明可以解决由非零和风险敏感随机微分博弈产生的“对角”二次倒向随机微分方程系统，这回答了El Karoui和Hamadène [Stochastic Process.]中提出的公开问题。107（2003），第164页]。
In this paper, we study a multi-dimensional BSDE with a “diagonally” quadratic generator, the quadratic part of whose i th component depends only on the i th row of the second unknown variable. Local and global solutions are given, which seem to be the first systematic (positive) results on the general solvability of multi-dimensional quadratic BSDEs. In our proofs, it is natural and crucial to apply both John–Nirenberg and reverse Hölder inequalities for BMO martingales. Our results are finally illustrated to solve the system of “diagonally” quadratic BSDEs arising from a nonzero-sum risk-sensitive stochastic differential game, which answers the open problem posed in El Karoui and Hamadène [Stochastic Process. Appl. 107 (2003), page 164].