Preface: Vicky Henderson & Ronnie Sircar -- Philip Protter: A Mathematical Theory of Financial Bubbles -- Fred Espen Benth: Stochastic Volatility and Dependency in Energy Markets – Multi-Factor Modelling -- Paolo Guasoni: Portfolio Choice with Transaction Costs: a User's Guide -- Dan Crisan: Cubature Methods and Applications.

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.