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R. J. Chitashvili and M. G. Mania, “Decomposition of the Maximum of Semimartingales and Generalized It’s Formula,” In: V. V. Sazonov and T. L. Shervashidze, Eds., New Trends in Probability and Statistics, Volume 1, Proceedings of the Bakuriani Colloquium in Honour of Yu. V. Prohorov, USSR, Bakuriani, 24 February-4 March 1990, pp. 301-350.

has been cited by the following article:

• TITLE: On Local Times: Application to Pricing Using Bid-Ask

  AUTHORS: Paul C. Kettler, Olivier Menoukeu-Pamen, Frank Proske

  KEYWORDS: Order Statistics; Semimartingales; Local Times; Arbitrage

  JOURNAL NAME: Journal of Mathematical Finance, Vol.4 No.2, February 19, 2014

  ABSTRACT: In this paper, we derive the evolution of a stock price from the dynamics of the “best bid” and “best ask”. Under the assumption that the bid and ask prices are described by semimartingales, we study the completeness and the possibility for arbitrage on such a market. Further, we discuss (insider) hedging for contingent claims with respect to the stock price process.