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arXiv · 1106.1400

Minimal supersolutions of convex BSDEs

Samuel Drapeau·Gregor Heyne·Michael Kupper
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Abstract

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.

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Samuel Drapeau, Gregor Heyne, Michael Kupper. 2011-06-07. Minimal supersolutions of convex BSDEs. https://doi.org/10.1214/13-aop834

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