<P>THE CURRENT VOLUME PRESENTS FOUR CHAPTERS TOUCHING ON SOME OF THE MOST IMPORTANT AND MODERN AREAS OF RESEARCH IN MATHEMATICAL FINANCE: ASSET PRICE BUBBLES (BY PHILIP PROTTER); ENERGY MARKETS (BY FRED ESPEN BENTH); INVESTMENT UNDER TRANSACTION COSTS (BY PAOLO GUASONI AND JOHANNES MUHLE-KARBE); AND NUMERICAL METHODS FOR SOLVING STOCHASTIC EQUATIONS (BY DAN CRISAN, K. MANOLARAKIS AND C. NEE).THE PARIS-PRINCETON LECTURE NOTES ON MATHEMATICAL FINANCE, OF WHICH THIS IS THE FIFTH VOLUME, PUBLISH CUTTING-EDGE RESEARCH IN SELF-CONTAINED, EXPOSITORY ARTICLES FROM RENOWNED SPECIALISTS. THE AIM IS TO PRODUCE A SERIES OF ARTICLES THAT CAN SERVE AS AN INTRODUCTORY REFERENCE SOURCE FOR RESEARCH IN THE FIELD. </P>

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The current volume presents four chapters touching on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy markets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Manolarakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.

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