Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches

17 Pages Posted: 20 Mar 2003

See all articles by Peter Imkeller

Peter Imkeller

Humboldt University of Berlin - Department of Mathematics

Abstract

We consider simple models of financial markets with regular traders and insiders possessing some extra information hidden in a random variable that is accessible to the regular trader only at the end of the trading interval. The problems we focus on are the calculation of the additional utility of the insider and a study of his free lunch possibilities. The information drift - that is, the drift to eliminate in order to preserve the martingale property in the insider's filtration - turns out to be the crucial quantity needed to answer these questions. It is most elegantly described by the logarithmic Malliavin trace of the conditional laws of the insider information with respect to the filtration of the regular trader. Several examples are given to illustrate additional utility and free lunch possibilities. In particular, if the insider has advance knowledge of the maximal stock price process, given by a regular diffusion, arbitrage opportunities exist.

Keywords: Insider Training, Enlargement of Filtrations, Malliavin's Calculus, Free Lunch, Arbitrage, Equivalent Martingale Measure, Bessel Process

Suggested Citation

Imkeller, Peter, Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches. Available at SSRN: https://ssrn.com/abstract=371404

Peter Imkeller (Contact Author)

Humboldt University of Berlin - Department of Mathematics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

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