Talks (titles and abstracts)
Beatrice Acciaio: Causal transport plans: duality and applications
Causal transport plans between two Polish filtered probability spaces \((X,(F^X_t),\mu)\) and \((Y,(F^Y_t),\nu)\) correspond to probability measures on \(X \times Y\) having the prescribed marginals \(\mu, \nu\), and such that the regular conditional kernel with respect to the fist coordinate satisfies a certain measurability condition. Roughly speaking: the amount of "mass" transported to a subset of the target space \(Y\) belonging to \(F^Y_t\), is solely determined by the information contained in \(F^X_t\).
Given a cost function on \(X \times Y\), the (primal) causal transport problem consists in minimizing the cost of transportation along causal transport plans. The characterization of the causality property via infinitely many linear constraints naturally leads to the formulation
of a dual problem. For a prominent class of cost functions, I will further identify a non-linear dual problem which we can fully solve.
This gives a proof of the semimartingale preservation property, and is achieved only through optimal transport and convex analysis techniques.
I will show duality results between the primal and the two dual problems, and some applications to finance.
The talk is based on joint works with J. Backhoff and A. Zalashko.
Bruno Bouchard: A randomization approach towards a super-hedging duality in model with transaction costs and uncertainty
Joint with Xiaolu Tan and Shuoqing Deng.
Matteo Burzoni: Model Independent pricing-hedging duality with transaction costs
Marco Frittelli: Disentangling Price, Risk and Model Risk
We propose a method to assess the intrinsic risk carried by a financial position when the agent faces uncertainty about the pricing rule providing its present value. Our construction is inspired by a new interpretation of the quasiconvex duality and naturally leads to the introduction of the general class of Value&Risk measures.
David Hobson: Robust hedging of American Puts
Michael Kupper: Duality formulas for robust hedging in discrete and continuous time
Marco Maggis: Pointwise Arbitrage Pricing Theory in Discrete Time
Marcel Nutz: Multiperiod Martingale Transport
Jan Obloj: On structure of martingale transports in arbitrary finite dimensions
We study the structure of martingale transports in finite dimensions. We consider the family \(\mathcal{M}(\mu,\nu)\) of martingale measures on \(\mathbb{R}\times \mathbb{R}\) with given marginals \(\mu,\nu\), and construct a family of relatively open convex sets \(\{C_x:x\in \mathbb{R}\}\), which forms a partition of \(\\mathbb{R}\), and such that any martingale transport in \(\mathcal{M}(\mu,\nu)\) sends mass from \(x\) to within \(\overline{C_x}, \mu(dx)\)--a.e. Our results extend the analogous one-dimensional results of Beiglböck and Juillet (2016) and Beiglböck, Nutz and Touzi (2017). We conjecture that the decomposition is canonical and minimal in the sense that it allows to characterise the martingale polar sets, i.e. the sets which have zero mass under all measures in \(\mathcal{M}(\mu,\nu)\).
This is joint, and ongoing, work with Pietro Siorpaes (Imperial College London)
Dylan Possamaï: TBA
Walter Schachermayer: Portfolio optimization with random endowment: the value-function may fail to be smooth
Mete Soner: Constrained Optimal Transport
Xiaolu Tan: Duality in nondominated discrete-time models for American options
Nizar Touzi: Infinite horizon Principal Agent problem, and random maturity second order backward SDEs