Optimal Skorokhod embedding given full marginals and Azéma -Yor peacocks *

International audienceWe consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0, 1]. The problem is related to the study of extremal martingales associated with a peacock (" process increasing in convex order " , by Hirsch, Profeta, Roynette and Yor [16]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the martingale transport problem studied in Henry-Labord ere, Ob lój , Spoida and Touzi [13]. Under technical conditions, some explicit characteristics of the solutions to the optimal SEP as well as to its dual problem are obtained. We also discuss the associated martingale inequality

Adapted Wasserstein distance between the laws of SDEs

We consider the adapted optimal transport problem between the laws of Markovian stochastic differential equations (SDE) and establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals an interesting connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes.Comment: 30 pages, 2 figures. Additional example adde

Model-independent bounds for Asian options:A dynamic programming approach

We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model-independent pricing in that we consider the problem as a dynamic programming problem, where the controlled process is the conditional distribution of the asset at the maturity date. By formulating the problem in this manner, we are able to determine the model-independent price through a PDE formulation. Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to generalise to many related problems

Model-independent bounds for Asian options - a dynamic programming approach

We consider the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our method differs from most approaches to model-independent pricing in that we consider the problem as a dynamic programming problem, where the controlled process is the conditional distribution of the asset at the maturity date. By formulating the problem in this manner, we are able to determine the model-independent price through a PDE formulation. Notably, this approach does not require specific constraints on the payoff function (e.g. convexity), and would appear to be generalisable to many related problems. (This is joint work with A.M.G. Cox.)Non UBCUnreviewedAuthor affiliation: École PolytechniquePostdoctora

Measure-valued martingales and optimality of solutions to the Skorokhod embedding problem

Non UBCUnreviewedAuthor affiliation: TU WienPostdoctora