Generalized BSDE With 2-Reflecting Barriers and Stochastic Quadratic Growth

2008/05/19 by El Hassan Essaky, Essaky, E. H., M. Hassani +1
Economics, Econometrics and Finance · Mathematics · #60H10 #60H20 #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0805.2979

openalex publication_date 2008/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the existence of a solution for a one-dimensional generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under assumptions on the input data which are weaker than that on the current literature. In particular, we construct a maximal solution for such a GRBSDE when the terminal condition ξis only F_T-measurable and the driver f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the variable z without assuming any P-integrability conditions. The work is suggested by the interest the results might have in Dynkin game problem and American game option.

Citations

• Conjugate convex functions in optimal stochastic control

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