Open Access
November 2013 Minimal supersolutions of convex BSDEs
Samuel Drapeau, Gregor Heyne, Michael Kupper
Ann. Probab. 41(6): 3973-4001 (November 2013). DOI: 10.1214/13-AOP834


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. "Minimal supersolutions of convex BSDEs." Ann. Probab. 41 (6) 3973 - 4001, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1284.60116
MathSciNet: MR3161467
Digital Object Identifier: 10.1214/13-AOP834

Primary: 60H10
Secondary: 34F05

Keywords: nonlinear expectations , Supermartingales , Supersolutions of backward stochastic differential equations

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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