A model-free approach to continuous-time finance
Mathematical Finance
2022-12-05 v1
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.
Keywords
Cite
@article{arxiv.2211.15531,
title = {A model-free approach to continuous-time finance},
author = {Henry Chiu and Rama Cont},
journal= {arXiv preprint arXiv:2211.15531},
year = {2022}
}