This volume contains survey papers on mathematical finance based on some courses given at the ""Lluis Santalo"" Summer School of the Real Sociedad Matematica Espanola, held in July 2007 at the Universidad Internacional Menendez Pelayo, Santander (Spain). The primary topics are pathwise approximations of stochastic differential equations, Hedge funds, and credit derivatives. The paper by L. Seco and F. Chen provides a systematic survey of hedge funds from a rigorous mathematical point of view. The related paper by M. Escobar, S. Kramer, F. Scheibl, L. Seco and R. Zagst introduces a new theoretical framework for the pricing of hedge funds' equity, inspired by the framework of Black and Cox for the valuation of company equity as a call option. A general framework for deriving high order, stable and tractable path-wise approximations of Stratonovich stochastic differential equations as applied to finance is the subject of the paper of L. G. Gyurko and T. Lyons. The paper by R. Zagst and M. Scherer is a short course on the different approaches used for pricing, hedging and risk management of credit derivatives. Researchers and practitioners in mathematical finance will find in this book a collection of excellent, up-to-date and mathematically rigorous presentations of some of the most advanced techniques for pricing and risk management. A co-publication of the AMS and Real Sociedad Matematica Espanola (RSME). Table of Contents: M. Escobar, S. Kramer, F. Scheibl, L.A. Seco, and R. Zagst -- Hedge funds as knock-out options; L. G. Gyurko and T. Lyons -- Rough paths based numerical algorithms in computational finance; L. A. Seco and F. Chen -- Hedge funds; R. Zagst and M. Scherer -- Modeling and pricing credit derivatives. (CONM/515)