Minimal supersolutions of convex BSDEs under constraints

Gregor Heyne, Michael Kupper, Christoph Mainberger, Ludovic Tangpi

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)178-195
Number of pages18
JournalESAIM - Probability and Statistics
Volume20
DOIs
StatePublished - Jan 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Duality
  • Gamma constraints
  • Minimality under constraints
  • Supersolutions of backward stochastic differential equations

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