Related papers: Frictional martingale optimal transport and robust…
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 robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
The Fundamental Review of the Trading Book (FRTB) poses a significant challenge for exotic derivatives pricing, particularly for non-modelable risk factors (NMRF) where sparse market data leads to infinite audit bounds under classical…
While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of…
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…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
In this paper, a new approach for solving the problems of pricing and hedging derivatives is introduced in a general frictionless market setting. The method is applicable even in cases where an equivalent local martingale measure fails to…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions…
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schr\"odinger bridge problems. We establish duality…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…
We consider Merton's problem with proportional transaction costs. It is well known that the optimal investment strategy is characterized by two trading boundaries, the buy boundary and the sell boundary, between which lies the no-trading…
Given the marginal distribution information of the underlying asset price at two future times $T_1$ and $T_2$, we consider the problem of determining a model-free upper bound on the price of a class of American options that must be…
In a martingale optimal transport (MOT) problem mass distributed according to the law $\mu$ is transported to the law $\nu$ in such a way that the martingale property is respected. Beiglb\"ock and Juillet (On a problem of optimal transport…
Motivated by applications in model-free finance and quantitative risk management, we consider Fr\'echet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in…
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we…