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

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067233

Digital Object Identifier
doi:10.1214/EJP.v20-3758

Mathematical Reviews number (MathSciNet)
MR3438741

Zentralblatt MATH identifier
1332.60081

Subjects
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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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