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      Department of Systems Engineering and Engineering Management

                             The Chinese University of Hong Kong

 

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Date: 4:30pm to 5:30pm, April 20, 2017 (Thursday)

 

Title: Canonical Supermartingale Couplings

 

Speaker: Prof. Marcel Nutz, Statistics and Mathematics Departments, Columbia University.

 

Abstract:

 

Motivated by model-robust pricing bounds in mathematical finance, we study supermartingale couplings of market smiles. Two probability distributions in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are allowed as transports. Much like the Hoeffding-Frechet coupling of classical transport and its symmetric counterpart, the Antitone coupling, these can be characterized by order-theoretic minimality properties, as simultaneous optimal transports for certain classes of reward (or cost) functions, and through no-crossing conditions on their supports. However, our two couplings have asymmetric geometries due to the directed nature of the supermartingale constraint. (Based on joint works with M. Beiglbock, F. Stebegg, N. Touzi)

 

Biography:

 

Marcel's research focuses on mathematical finance, probability theory and stochastic optimal control. He obtained his PhD from ETH Zurich and is currently an Associate Professor and Alfred P. Sloan Fellow at Columbia University's Statistics and Mathematics departments.

 

This seminar is hosted by Prof. HE Xuedong.

 

Everyone is welcome to attend the talk!

 

 

Venue: Room 1009,

      William M.W. Mong Engineering Building (ERB),

      The Chinese University of Hong Kong.

 

SEEM-5202 Website: http://seminar.se.cuhk.edu.hk

Email: seem5202@se.cuhk.edu.hk