Electronic Journal of Probability

An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift

Alexander Fromm, Peter Imkeller, and David Prömel

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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 Equation (FBSDE), 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 FBSDE to a setting in which the coefficients are only locally Lipschitz continuous.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 127, 38 pp.

Received: 28 August 2014
Accepted: 8 December 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 93E20: Optimal stochastic control

BMO process BSDE decoupling field forward backward stochastic differential equation FBSDE Skorokhod embedding variational differentiation

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Fromm, Alexander; Imkeller, Peter; Prömel, David. An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift. Electron. J. Probab. 20 (2015), paper no. 127, 38 pp. doi:10.1214/EJP.v20-3758. https://projecteuclid.org/euclid.ejp/1465067233

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