Talks (titles and abstracts)

Mathias Beiglböck: Optimal Transport and Skorokhod Embedding

Model-independent pricing has grown into an independent field in Mathematical Finance during the last 15 years. A driving inspiration in this area has been the fruitful connection to the Skorokhod embedding problem. We discuss a link between Skorokhod's problem and the more recent optimal transport approach to model-independent pricing.

Patrick Cheridito: Dual representation of increasing convex functionals with sigma-additive measures

It follows from standard convex duality arguments that increasing convex functionals on spaces of bounded measurable functions have a dual representation with finitely additive measures. In this talk, a new sequential continuity condition is introduced that allows to derive dual representation results with sigma-additive measures.

Yan Dolinsky: Hedging with Friction and Volatility Uncertainty: Duality and Asymptotic

We consider a discrete time setup of model uncertainty. In this setup we study super-replication of European options under general friction. This problem is the model free version of previous work with Mete Soner (Duality and Convergence for Binomial Markets with Friction).
We generalize the duality for the model free setup and establish Asymptotics for the super-replication prices.
Joint work with Selim Gokay and Peter Bank.

Samuel Drapeau: Preference for Averages: Different but Intricate Dimensions of Uncertainty Aversion

We study the preferences of agents for averages and better outcomes when they are facing both, in Frank Knight's formulation, measurable as well as unmeasurable uncertainty.
Following Anscombe and Aumann, such a situation can be modeled by preferences expressed on stochastic kernels, that is scenario dependent lotteries.
By means of automatic continuity methods based on Banach-Dieudonné's Theorem on Fréchet spaces, we provide a robust representation. This gives us some insight into the nature of uncertainty aversion these preferences are expressing.
We further investigate under which conditions these two intricate dimensions of uncertainty can be disentangle into a distributional uncertainty, in the direction of von Neumann and Morgenstern's theory, and a probability model uncertainty, in the spirit of risk measures. These results allow in particular to address both Allais as well as Elsberg's paradox.
Joint work with P. Cheridito, F. Delbaen, and M. Kupper.

Fabio Maccheroni: The Hahn-Banach Theorem for modules over f-algebras

Vincent-Smith (1967) considers an extremally disconnected compact Hausdorff space \(S\) and obtains a perfect analogue of the Hahn-Banach Theorem for modules over \(C(S)\). Filipovic, Kupper, and Vogelpoth (2009) obtain the same result for modules over the algebra \(M(S,F,m)\) of (equivalence classes of) measurable functions.
Here we show that these results can be extended to the most important common generalization of \(C(S)\) and \(M(S,F,m)\): a Dedekind complete f-algebra with multiplicative unit.
As corollaries we obtain the analogue of the Kantorovich Extension Theorem and we are able to generalize the dual pairs theory of Dieudonne and Mackey to this class of modules.
Joint work with Simone Cerreia-Vioglio and Massimo Marinacci.

Marcel Nutz: Nonlinear Levy Processes and their Characteristics

 

Jan Obloj: Robust pricing-hedging duality with no-short selling constraints and emergence of bubbles

 

Ludovic Tangpi: Fundamental theorem of asset pricing without reference measure

In this talk, we focus on the fundamental theorem of asset pricing in the case where the market is governed by a non-dominated set of probability measures. We introduce the concept of local arbitrage. Our main result shows that, in a continuous time model, if the agent is allowed to trade only with strategies that are simple integrands, then the absence of local arbitrage can be characterized by the existence of a set of local martingale measures equivalent to the set of possible models.
Talk based on a join work with Michael Kupper and Patrick Cheridito.

Nizar Touzi: On the dual formulation of the optimal martingale transport problem

 

JavaScript has been disabled in your browser