Related papers: Martingale Optimal Transport and Robust Hedging in…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
A convex duality result for martingale optimal transport problems with two marginals was established in Beiglb\"ock et al. (2013). In this paper we provide a generalization of this result to the multi-period setting.
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the…
We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the…
This paper investigates causal optimal transportation problems, in the framework of two Polish spaces, both endowed with filtrations. Specific concretizations yield primal problems equivalent to several classical problems of stochastic…
In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and…
Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
It is well known that martingale transport plans between marginals $\mu\neq\nu$ are never given by Monge maps -- with the understanding that the map is over the first marginal $\mu$, or forward in time. Here, we change the perspective, with…
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the…
Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.…
We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an…
This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation of productions over factories, a distribution of sales…
We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…