Multidimensional Backward Stochastic Differential Equations with Left-Lipschitz Coefficients

J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 1, Page 115–126.

Xu, Yuhong
Multidimensional Backward Stochastic Differential Equations with Left-Lipschitz Coefficients
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Abstract:
In this note, we consider multidimensional backward stochastic differential equations with coefficients which are left-Lipschitz w.r.t. $y$ and Lipschitz w.r.t. $z$ and without explicit constraints on the growth. An existence theorem of minimal solution is established in this framework. We also relate it to the hedging problem for interacting economic agents.

Keywords: Backward stochastic differential equation, discontinuous coefficient, minimal solution, maximal solution.

Mathematics Subject Classification (2010): 60H10.
Mathematical Reviews Number: MR3112088

Received: 2012-08-20