Martingale Optimal Transport with Stopping

SIAM Journal on Control and Optimization, Forthcoming

18 Pages Posted: 3 Mar 2017 Last revised: 24 Nov 2017

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Alexander Cox

University of Bath

Yavor Stoev

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: November 22, 2017

Abstract

We solve the martingale optimal transport problem for cost functionals represented by optimal stopping problems. The measure-valued martingale approach developed in [A. M. G. Cox and S. Kallblad. Model-independent bounds for Asian options: a dynamic programming approach. SIAM Journal on Control and Optimization, 55(6):3409–3436, 2017.] allows us to obtain an equivalent infinite-dimensional controller-stopper problem. We use the stochastic Perron's method and characterize the finite dimensional approximation as a viscosity solution to the corresponding HJB equation. It turns out that this solution is the concave envelope of the cost function with respect to the atoms of the terminal law. We demonstrate the results by finding explicit solutions for a class of cost functions.

Keywords: martingale optimal transport, dynamic programming, optimal stopping, stochastic Perron method, viscosity solutions, concave envelope, distribution constraints

JEL Classification: C73

Suggested Citation

Bayraktar, Erhan and Cox, Alexander and Stoev, Yavor, Martingale Optimal Transport with Stopping (November 22, 2017). SIAM Journal on Control and Optimization, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2926552 or http://dx.doi.org/10.2139/ssrn.2926552

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Alexander Cox

University of Bath ( email )

Yavor Stoev (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

3863 East Hall
530 Church Street
Ann Arbor, MI 48109
United States

HOME PAGE: http://www-personal.umich.edu/~ystoev/

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