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A model-free approach to continuous-time finance

Title: A model-free approach to continuous-time finance
Authors: Chiu, H
Cont, R
Item Type: Journal Article
Abstract: We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral (every self-financing strategy is a gradient) and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
Issue Date: Apr-2023
Date of Acceptance: 16-Nov-2022
URI: http://hdl.handle.net/10044/1/101307
DOI: 10.1111/mafi.12370
ISSN: 0960-1627
Publisher: Wiley
Start Page: 257
End Page: 273
Journal / Book Title: Mathematical Finance
Volume: 33
Issue: 2
Copyright Statement: © 2023 The Authors. Mathematical Finance published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Publication Status: Published
Online Publication Date: 2023-01-16
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences
Mathematics



This item is licensed under a Creative Commons License Creative Commons