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On Local Times: Application to Pricing Using Bid-Ask
Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway
Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, Liverpool, UK
Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway
- 1 Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway
- 2 Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, Liverpool, UK
- 3 Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway
Journal of Mathematical Finance·Volume 04 (2014)·Pages 84–94·Published 14 February 2014·DOI10.4236/jmf.2014.42008
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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 .
KeywordsOrder StatisticsSemimartingalesLocal TimesArbitrage
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