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An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift. (English) Zbl 1332.60081
Summary: We solve the Skorokhod embedding problem for a class of Gaussian processes including Brownian motion with non-linear drift. Our approach relies on solving an associated strongly coupled system of forward backward stochastic differential equations (FBSDEs), and investigating the regularity of the obtained solution. For this purpose we extend the existence, uniqueness and regularity theory of so called decoupling fields for Markovian FBSDEs to a setting in which the coefficients are only locally Lipschitz continuous.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G40 Stopping times; optimal stopping problems; gambling theory
60G15 Gaussian processes
60H30 Applications of stochastic analysis (to PDEs, etc.)
93E20 Optimal stochastic control
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