Local times for typical price paths and pathwise Tanaka formulas

2014/05/31 by Nicolas Perkowski, David J. Prömel · 32 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Discrete time and continuous time #Economic theories and models #Finance #Financial Markets and Investment Strategies #Mathematical finance #Mathematics #Pure mathematics #Statistics #Stochastic processes and financial applications #math.PR #msc:60H05 #msc:60J60. #msc:91G99 #q-fin.MF

paper · pdf · doi:10.1214/ejp.v20-3534

published in Electronic Journal of Probability 20(none) (Institute of Mathematical Statistics)

openalex publication_date 2015/01/01 · arxiv created 2015/04/19 · arxiv updated 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 α-Hölder continuous for all α < 1/2. Additionally, we provide various generalizations of Föllmer's pathwise Itô formula.

Citations

• Differential equations driven by rough signals
• An inequality of the Hölder type, connected with Stieltjes integration
• The Existence of Dominating Local Martingale Measures

Cited by

• On pathwise quadratic variation for càdlàg functions