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Minimal Supersolutions of Convex BSDEs under Constraints

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2013

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Heyne, Gregor
Mainberger, Christoph

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http://nbn-resolving.de/urn:nbn:de:bsz:352-264108
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http://arxiv.org/abs/1311.6910

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Zusammenfassung

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 L1-lower semicontinuity. Furthermore, we provide duality results within the present framework and thereby give conditions for the existence of solutions under constraints.

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510 Mathematik

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ISO 690HEYNE, Gregor, Michael KUPPER, Christoph MAINBERGER, Ludovic TANGPI, 2013. Minimal Supersolutions of Convex BSDEs under Constraints
BibTex
@unpublished{Heyne2013Minim-26410,
  year={2013},
  title={Minimal Supersolutions of Convex BSDEs under Constraints},
  author={Heyne, Gregor and Kupper, Michael and Mainberger, Christoph and Tangpi, Ludovic}
}
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