Ito calculus without probability in idealized financial markets

2011/08/03 by Vladimir Vovk, Vovk, Vladimir · 1 citation
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Mathematical and Theoretical Analysis #Stochastic processes and financial applications #math.PR #msc:60G05 #msc:60G17 #msc:60G44 #msc:91G99 #q-fin.TR

paper · pdf · doi:10.48550/arxiv.1108.0799

29 pages

arxiv created 2014/08/29 · arxiv updated 2014/09/01

Abstract

We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths, where the qualification "typical" means that there is a trading strategy that risks only one monetary unit and brings infinite capital if quadratic variation does not exist. This result allows one to apply numerous known results in pathwise Ito calculus to typical price paths; we give a brief overview of such results.

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• The Itô-Föllmer formula -- nonstandard cases

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