Rough paths in idealized financial markets
نویسنده
چکیده
This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2; in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is right-continuous. The qualification “typical” means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.
منابع مشابه
Rough paths in idealized financial markets (draft)
This note is a review of known results about the paths of security prices in idealized financial markets that satisfy a version of the no-arbitrage condition. Without making any probabilistic assumptions, it is sometimes possible to characterize the roughness of the price paths. A few simple new results are also stated.
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تاریخ انتشار 2010