2021/06/14 by Zhengqing Zhou, Zhou, Zhengqing, José Blanchet +4
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.OC #math.PR #math.ST #q-fin.CP #stat.TH
paper · pdf · doi:10.48550/arxiv.2106.07191
openalex publication_date 2021/06/14 · arxiv created 2021/11/30 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of bounding path-dependent expectations (within any finite time horizon d) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark marginal distributions. This problem is a relaxation of the martingale optimal transport (MOT) problem and is motivated by applications to super-hedging in financial markets. We show that the empirical version of our relaxed MOT problem can be approximated within O( n-1/2) error where n is the number of samples of each of the individual marginal distributions (generated independently) and using a suitably constructed finite-dimensional linear programming problem.