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arXiv:1106.1400 [math.PR]AbstractReferencesReviewsResources

Minimal supersolutions of convex BSDEs

Samuel Drapeau, Gregor Heyne, Michael Kupper

Published 2011-06-07, updated 2013-12-13Version 4

We study the nonlinear operator of mapping the terminal value $\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.

Comments: Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2013, Vol. 41, No. 6, 3973-4001
Categories: math.PR
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