Martingale optimal transport with stopping

Erhan Bayraktar, Alexander M.G. Cox, Yavor Stoev

Research output: Contribution to journalArticle

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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. Källblad, SIAM J. Control Optim., 55 (2017), pp. 3409–3436] 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.

Original languageEnglish
Pages (from-to)417-433
Number of pages17
JournalSIAM Journal on Control and Optimization
Volume56
Issue number1
Early online date13 Feb 2018
DOIs
Publication statusPublished - 2018

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Optimal Transport
Martingale
Cost functions
Cost Function
HJB Equation
Finite-dimensional Approximation
Optimal Stopping Problem
Viscosity Solutions
Explicit Solution
Envelope
Viscosity
Controller
Atoms
Controllers
Costs
Demonstrate
Class

Keywords

  • math.PR
  • 60G40, 93E20, 91A10, 91A60, 60G07

Cite this

Martingale optimal transport with stopping. / Bayraktar, Erhan; Cox, Alexander M.G.; Stoev, Yavor.

In: SIAM Journal on Control and Optimization, Vol. 56, No. 1, 2018, p. 417-433.

Research output: Contribution to journalArticle

Bayraktar, Erhan ; Cox, Alexander M.G. ; Stoev, Yavor. / Martingale optimal transport with stopping. In: SIAM Journal on Control and Optimization. 2018 ; Vol. 56, No. 1. pp. 417-433.
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