Local times for typical price paths and pathwise Tanaka formulas

Abstract

Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is $\alpha$-Hölder continuous for all $\alpha <1/2$. Additionally, we provide various generalizations of Föllmer's pathwise Itô formula.

References in corpus (5)

• Continuous-time trading and the emergence of probability
• Hedging under arbitrage
• Two-parameter $p,q$-variation Paths and Integrations of Local Times
• Rough paths in idealized financial markets
• The Existence of Dominating Local Martingale Measures

Cited by in corpus (10)

• Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity
• Pathwise integration with respect to paths of finite quadratic variation
• Trading Strategies Generated Pathwise by Functions of Market Weights
• On pathwise quadratic variation for cadlag functions
• Local times and Tanaka--Meyer formulae for càdlàg paths
• Efficient discretisation of stochastic differential equations
• Local times for continuous paths of arbitrary regularity
• Another example of duality between game-theoretic and measure-theoretic probability
• Itô--Föllmer Calculus in Banach Spaces I: The Itô Formula
• Non-stochastic portfolio theory