Existence, minimality and approximations of solutions of BSDEs with convex drivers

P. Cheridito, M.A. Stadje

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1540-1565
JournalStochastic Processes and their Applications
Volume122
Issue number4
DOIs
Publication statusPublished - 2012

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