Continuous-time trading and the emergence of probability
نویسندگان
چکیده
منابع مشابه
Continuous-time trading and the emergence of probability
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price process, without making any stochastic assumptions. It is shown that almost all sample paths of the price process possess quadratic variation, where “almost ...
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A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on “qualitative” results, stated in terms of order (or order topology) rather than in terms of the precise values taken by the price p...
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This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.
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A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on “qualitative” results, stated in terms of order (or order topology) rather than in terms of the precise values taken by a price pro...
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This note is part of the recent revival of interest in game-theoretic probability (see, e.g., [7, 8, 4, 2, 3]). It concentrates on the study of the“ √ dt effect”, the fact that a typical change in the value of a non-degenerate diffusion process over short time period dt has order of magnitude √ dt. Within the “standard” (not using non-standard analysis) framework of game-theoretic probability, ...
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ژورنال
عنوان ژورنال: Finance and Stochastics
سال: 2012
ISSN: 0949-2984,1432-1122
DOI: 10.1007/s00780-012-0180-5