E-Book Overview
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)
E-Book Content
CONTEMPORARY MATHEMATICS 515
Mathematics in Finance UIMP-RSME Lluis A. Santaló Summer School Mathematics in Finance and Insurance July 16–20, 2007 Universidad Internacional Menéndez Pelayo Santander, Spain
Santiago Carrillo Menéndez José Luis Fernández Pérez Editors
American Mathematical Society Real Sociedad Matemática Española
American Mathematical Society
Mathematics in Finance
This page intentionally left blank
CONTEMPORARY MATHEMATICS 515
Mathematics in Finance UIMP-RSME Lluis A. Santaló Summer School Mathematics in Finance and Insurance July 16–20, 2007 Universidad Internacional Menéndez Pelayo Santander, Spain
Santiago Carrillo Menéndez José Luis Fernández Pérez Editors
American Mathematical Society Real Sociedad Matemática Española
American Mathematical Society Providence, Rhode Island
Editorial Board of Contemporary Mathematics Dennis DeTurck, managing editor George Andrews
Abel Klein
Martin J. Strauss
Editorial Committee of the Real Sociedad Matem´ atica Espa˜ nola Guillermo P. Curbera, Director Luis Al´ıas Linares Emilio Carrizosa Priego Bernardo Cascales Salinas Javier Duoandikoetxea Zuazo
Alberto Elduque Palomo Pablo Pedregal Tercero Rosa Mar´ıa Mir´ o-Roig Juan Soler Vizca´ıno
2000 Mathematics Subject Classification. Primary 91G20, 91G40, 91G60, 91G80, 65C30, 60H10.
Library of Congress Cataloging-in-Publication Data UIMP-RSME Santal´ o Summer School (2007 : Universidad Internacional Men´endez Pelayo) Mathematics in finance : UIMP-RSME Lluis A. Santal´ o Summer School, mathematical finance and insurance, July 16–20, 2007, Universidad Internacional Men´endez Pelayo, Santander, Spain / Santiago Carrillo Men´ endez, Jos´ e Luis Fern´ andez P´ erez, editors. p. cm. — (Contemporary mathematics : v. 515) Includes bibliographical references. ISBN 978-0-8218-4673-5 (alk. paper) 1. Finance—Mathematical models—Congresses. I. Carrillo Men´ endez, Santiago, 1950– II. Fern´ andez P´erez, Jos´ e Luis. III. American Mathematical Society. IV.