## The Annals of Probability

### Minimal supersolutions of convex BSDEs

#### 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.

#### Article information

Source
Ann. Probab., Volume 41, Number 6 (2013), 3973-4001.

Dates
First available in Project Euclid: 20 November 2013

https://projecteuclid.org/euclid.aop/1384957780

Digital Object Identifier
doi:10.1214/13-AOP834

Mathematical Reviews number (MathSciNet)
MR3161467

Zentralblatt MATH identifier
1284.60116

#### Citation

Drapeau, Samuel; Heyne, Gregor; Kupper, Michael. Minimal supersolutions of convex BSDEs. Ann. Probab. 41 (2013), no. 6, 3973--4001. doi:10.1214/13-AOP834. https://projecteuclid.org/euclid.aop/1384957780

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