Minimal Supersolutions of Convex BSDEs under Constraints

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HEYNE, Gregor, Michael KUPPER, Christoph MAINBERGER, Ludovic TANGPI, 2013. Minimal Supersolutions of Convex BSDEs under Constraints

@unpublished{Heyne2013Minim-26410, title={Minimal Supersolutions of Convex BSDEs under Constraints}, year={2013}, author={Heyne, Gregor and Kupper, Michael and Mainberger, Christoph and Tangpi, Ludovic} }

Tangpi, Ludovic We study supersolutions of a backward stochastic differential equation, the control processes of which are constrained to be continuous semimartingales of the form dZ=Δdt+ΓdW. The generator may depend on the decomposition (Δ,Γ) and is assumed to be positive, jointly convex and lower semicontinuous, and to satisfy a superquadratic growth condition in Δ and Γ. We prove the existence of a supersolution that is minimal at time zero and derive stability properties of the non-linear operator that maps terminal conditions to the time zero value of this minimal supersolution such as monotone convergence, Fatou's lemma and L<sup>1</sup>-lower semicontinuity. Furthermore, we provide duality results within the present framework and thereby give conditions for the existence of solutions under constraints. Kupper, Michael terms-of-use 2014-02-24T10:33:46Z Mainberger, Christoph eng 2014-02-24T10:33:46Z Kupper, Michael Heyne, Gregor Mainberger, Christoph Minimal Supersolutions of Convex BSDEs under Constraints Tangpi, Ludovic 2013 Heyne, Gregor

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