We study the optimal transport between two probability measures on the real line, where the
transport plans are laws of one-step martingales. A quasi-sure formulation of the dual …

This book develops a mathematical theory for finance, based on a simple and intuitive
absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial …

Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation
of model-independent bounds for exotic options consistent with market prices of liquid …

We consider a stochastic control problem for a class of nonlinear kernels. More precisely,
our problem of interest consists in the optimization, over a set of possibly nondominated …

We pursue a robust approach to pricing and hedging in mathematical finance. We consider
a continuous-time setting in which some underlying assets and options, with continuous …

We obtain a dual representation of the Kantorovich functional defined for functions on the
Skorokhod space using quotient sets. Our representation takes the form of a Choquet …

We develop a one-dimensional notion of affine processes under parameter uncertainty,
which we call nonlinear affine processes. This is done as follows: given a set Θ of …

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 SS …

An unconventional approach for optimal stop** under model ambiguity is introduced.
Besides ambiguity itself, we take into account how ambiguity‐averse an agent is. This …

We provide an extension of the martingale version of the Fréchet–Hoeffding coupling to the
infinitely-many marginals constraints setting. In the two-marginal context, this extension was …