Minimal supersolutions of convex BSDEs under constraints

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HEYNE, Gregor, Michael KUPPER, Christoph MAINBERGER, Ludovic TANGPI, 2016. Minimal supersolutions of convex BSDEs under constraints. In: ESAIM : Probability and Statistics. 20, pp. 178-195. ISSN 1292-8100. eISSN 1262-3318

@article{Heyne2016-07-14Minim-37456, title={Minimal supersolutions of convex BSDEs under constraints}, year={2016}, doi={10.1051/ps/2016011}, volume={20}, issn={1292-8100}, journal={ESAIM : Probability and Statistics}, pages={178--195}, author={Heyne, Gregor and Kupper, Michael and Mainberger, Christoph and Tangpi, Ludovic} }

Kupper, Michael Heyne, Gregor 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. 2017-02-15T14:14:31Z Kupper, Michael Mainberger, Christoph Tangpi, Ludovic Heyne, Gregor Minimal supersolutions of convex BSDEs under constraints 2017-02-15T14:14:31Z Mainberger, Christoph Tangpi, Ludovic 2016-07-14 eng

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