2011/05/07 by Patrick Cheridito, Cheridito, Patrick, Mitja Stadje +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H10 #65C30 #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60H10 #msc:65C30
paper · pdf · doi:10.48550/arxiv.1105.1471
arxiv created 2011/05/07 · openalex publication_date 2011/05/07 · arxiv updated 2011/05/10 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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 existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions.