Type: Seminar

Distribution: World

Expiry: 27 Jan 2020

Auth: aksamit@paksamit.pc (assumed)

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