The Annals of Probability

Minimal supersolutions of convex BSDEs

Samuel Drapeau, Gregor Heyne, and Michael Kupper

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

First available in Project Euclid: 20 November 2013

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

Supersolutions of backward stochastic differential equations nonlinear expectations supermartingales


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

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