Related papers: Duality for pathwise superhedging in continuous ti…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
The martingale optimal transport aims to optimally transfer a probability measure to another along the class of martingales. This problem is mainly motivated by the robust superhedging of exotic derivatives in financial mathematics, which…
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given…
We establish a super-replication duality in a continuous-time financial model where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an…
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…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$.…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
The goal of this paper is to define stochastic integrals and to solve stochastic differential equations for typical paths taking values in a possibly infinite dimensional separable Hilbert space without imposing any probabilistic structure.…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets…
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to…
The objective of this paper is to develop a duality between a novel Entropy Martingale Optimal Transport problem (A) and an associated optimization problem (B). In (A) we follow the approach taken in the Entropy Optimal Transport (EOT)…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price…
In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural…