CRM: Centro De Giorgi
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Advances in Mathematical Finance and Optimal Transport

course: A model-free approach to continuous-time finance

speaker: Rama Cont (University of Oxford)

abstract: We present a non-probabilistic, pathwise framework to continuous-time finance based on non-anticipative functional calculus, an extension of Hans Follmer's pathwise Ito calculus to non-anticipative functionals 1. We exhibit a class of non-anticipative functionals, called Class M functionals, which play a role analogous to martingales in the pathwise theory. We provide a 'local' definition of the self-financing property, independent of any particular notion of integration, and show that the value of a self-financing portfolio is a class M functional. We formulate the notion of hedging cost across a set of scenarios and formulate a pathwise dynamic programming principle for the superhedging cost.

Joint work with Henry CHIU (Imperial College London).


1 H Chiu, R Cont (2019) Causal functional calculus. https:/arxiv.orgabs1912.07951

2 H Chiu, R Cont (2021) A model-free approach to continuous-time finance.

Tue 28 Jun, 15:15 - 16:00, Aula Dini
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