On the continuous dependence of the minimal solution of constrained backward stochastic differential equations

Details On the continuous dependence of the minimal solution of constrained backward stochastic differential equations On the continuous dependence of the minimal solution of constrained backward stochastic differential equations

2010-11-09

arxiv.org/abs/1011.1976v2

Mathematics

Probability

It seems that the result holds for more general cas, and it hard to give an counterexample!

Scientific paper

It is well-known that solutions of backward differential equations are continuously dependent on the terminal value. Since the increasing part of the minimal solution of a constrained backward differential equation (shortly CBSDE) varies against terminal value, the continuous dependence property of terminal value is not obvious for it. In this paper, we obtain a result about this problem under some mild assumptions. The main tool used here is the penalization method to get the minimal solution of a CBSDE and the property of convex functional that it is continuous when it is lower semi-continuous. The comparison theorem of the minimal solution of CBSDE plays a crucial role in our proof.

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