01-07-2015, ore 14:00 precise
Arbitrage theory without a reference probability: challenges of the model-free approach
- Arbitrage theory without a reference probability: challenges of the model-free approach
- Marco Maggis, Università degli Studi di Milano
- Mercoledì 1 luglio 2015 alle ore 14:00 precise, Aula Saleri (VI piano)
In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets, The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities.
Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.
Politecnico di Milano, Dipartimento di Matematica via Bonardi 9, 20133 Milano – Telefono: +39 02 2399 4505 – Fax: +39 02 2399 4568