Existence, minimality and approximation of solutions to BSDEs with convex drivers

Patrick Cheridito and Mitja Stadje ()

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1540-1565

Abstract: We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y,Z) with bounded Z if the terminal condition is Lipschitz in W and that it can be approximated by the solutions to properly discretized equations. If the terminal condition is bounded and uniformly continuous in W we show the existence of a minimal continuous supersolution by uniformly approximating the terminal condition with Lipschitz terminal conditions. Finally, we prove the existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions.

Keywords: Backward stochastic differential equations; Backward stochastic difference equations; Convex drivers; Discrete-time approximations; Supersolutions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2011.12.008

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