Stochastics and Finance Seminar: Ivan Guo -- Path-dependent optimal transport with applications

Speaker: Dr Ivan Guo (Monash) 

Title: Path-dependent optimal transport with applications

Abstract:  We introduce a generalisation of the classical martingale optimal transport 
problem that relaxes the usual marginal distribution constraints to arbitrary convex 
constraints on the space of probability measures. Duality is established, which leads 
to a path-dependent Hamilton-Jacobi-Bellman equation, in which the solution localises 
to the state variables of the constraints, while bypassing the usual dynamic programming 
principle.


Our result has a variety of applications, including: model calibration on path-dependent 
as well as VIX derivatives; admissibility of option prices (analogous to the first 
fundamental theorem of asset pricing); portfolio selection problems with target wealth 
distributions; and robust hedging in continuous time.

http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html