Itô Calculus without Probability in Idealized Financial Markets

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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.
Original languageEnglish
Pages (from-to)270-290
Number of pages21
JournalLithuanian Mathematical Journal
Issue number2
Publication statusE-pub ahead of print - 15 May 2015

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