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Title: Model-independence in a fixed-income market via weak optimal transport
Abstract: In this talk I will consider model-independent pricing problems in a stochastic interest rates framework. In this case the usual tools from Martingale Optimal Transport cannot be applied. I will show how some pricing problems in a fixed-income market can be reformulated as Weak Optimal Transport problems as introduced by Gozlan et al. (2017). This allows us to establish a first robust super-replication result in such a framework, and leads to a characterization of extremal pricing models.
This talk is based on joint work with M. Beiglboeck and G. Pammer.
Title: Zero-sum Dynkin games: from full to partial information
Abstract: I will review recent results on the impact that various information structures have on the solution of zero-sum Dynkin games in continuous time. I will start by illustrating the structure of optimal strategies in specific examples for players who are (i) fully informed, (ii) equally partially informed and (iii) asymmetrically partially informed. Then I will present general results on the existence of a value and of optimal strategies for non-Markovian Dynkin games with arbitrary information structure. If time allows I will also show by counterexamples that our assumptions are minimal.
(This talk is based on joint work with E. Ekstrom, F. Gensbittel, K. Glover, N. Merkulov, J. Palczewski, S. Villeneuve)
Title: Optimal Entropy-Transport Problems and Helinger-Kantorovich Distance
Abstract: The talk will present an overview of Optimal Transport between unbalanced finite positive measures, with a special focus on the Hellinger-Kantorovich distance, whose geometric properties play a similar role to the L^2-Wasserstein distance between probability measures.
Some aspects concerning primal and dual formulations, optimality conditions, and dynamic formulation will be addressed, with special emphasis on the links between continuity and Hamilton-Jacobi equations, which are particularly relevant for studying the geodesic convexity of entropy functionals (in collaboration with A. Mielke, M. Liero and G. Sodini)
Title: Swarm gradient dynamics for global optimization: the density case
Abstract: Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend the simulated annealing method to a wide class of global optimization methods. Due to an inbuilt combination of a gradient-like strategy and particles interactions, we call them swarm gradient dynamics. As in the original paper of Holley-Kusuoka- Stroock, the key to the existence of a schedule ensuring convergence to a global minimizer is a functional inequality. One of our central theoretical contributions is the proof of such an inequality for one-dimensional compact manifolds. We conjecture the inequality to be true in a much wider setting.
Joint work with J. Bolte and L. Miclo
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