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A model-free approach to continuous-time finance
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Mathematical Finance - 2023 - Chiu - A model‐free approach to continuous‐time finance.pdf | Published version | 296.09 kB | Adobe PDF | View/Open |
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