Related papers: A superhedging approach to stochastic integration

We prove that the model-free typical (in the sense of Vovk) c\`adl\`ag price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions…

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.…

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…

We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths,…

We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…

The purpose of this note is to prove the It{\^o}-F\"ollmer formula for the c\`adl\`ag paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions. By this we mean, for example, that we do not…

Using rough path theory, we provide a pathwise foundation for stochastic It\^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To…

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We…

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally…

Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…

Shafer and Vovk introduce in their book \cite{ShaferVovk:2018} the notion of \emph{instant enforcement} and \emph{instantly blockable} properties. However, they do not associate these notions with any outer measure, unlike what Vovk did in…

For a real c\`adl\`ag path $x$ we define sequence of semi-explicit quantities, which do not depend on any partitions and such that whenever $x$ is a path of a c\`adl\`ag semimartingale then these quantities tend a.s. to the continuous part…

In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling…

Based on a dyadic approximation of It\^o integrals, we show the existence of It\^o c\`adl\`ag rough paths above general semimartingales, suitable Gaussian processes and non-negative typical price paths. Furthermore, Lyons-Victoir extension…

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…

We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of quadratic variation, introduced by Veraar and Yaroslavtsev…

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted…

We prove a robust super-hedging duality result for path-dependent options on assets with jumps, in a continuous time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some…

New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We…