2017/03/25 by Vladimir Vovk, Vovk, Vladimir, Glenn Shafer +1
Decision Sciences · Economics, Econometrics and Finance · #60G05 (Secondary) #60G17 #91G99 (Primary) 60G44 #Economic theories and models #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1703.08715
openalex publication_date 2017/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard results in martingale theory, including the Dubins-Schwarz theorem, the Girsanov theorem, and results concerning the Itô integral. We also establish the existence of an equity premium and a CAPM relationship in this probability-free setting.