Rough paths in idealized financial markets

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 positive and 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.Comment: 21 pages, this version adds (in Appendix C) a reference to new results in the foundations of game-theoretic probability based on Hardin and Taylor's work on hat puzzle

Supporting ethical, independent learning behavior among university students in the Arabian Gulf

© Springer International Publishing Switzerland 2014. Students in the Arabian Gulf region and the world over confront plagiarism temptations wittingly or unwittingly due to the multitude of free and easily available electronic sources of information. Rather than develop independent learning skills and academic integrity, students are often taken advantage of by essay mills that sell readymade essays. Instructors at times compound the problem by repeatedly recycling course assignments and tasks. Furthermore, there have been reports of the use of social networking sites for outsourcing and contract cheating in student assignments. This paper discusses how educators in an institution of higher learning in the UAE assist students to develop good academic skills. Data collection is with the use of an online survey questionnaire. Concurring with Wheeler and Anderson (2010) who call for appropriate and comprehensive institutional policies and guidelines for dealing with plagiarism, practical examples of the processes and procedures used at these institutions are provided

Uniform convergence of the empirical spectral distribution function

AbstractLet X be a linear process having a finite fourth moment. Assume F is a class of square-integrable functions. We consider the empirical spectral distribution function Jn,X based on X and indexed by F. If F is totally bounded then Jn,X satisfies a uniform strong law of large numbers. If, in addition, a metric entropy condition holds, then Jn,X obeys the uniform central limit theorem

Matematinio ugdymo bendrojo ugdymo mokykloje gairės [elektroninis išteklius] : [2013 m. birželio 14 d.]

Projektas „Matematinio ugdymo kaitos gairės“Vilniaus universitetasVytauto Didžiojo universitetasŠvietimo akademij