real property In collaboration with the researchers at absolutely a high rate of S&F, he has published numerous articles in the johny too raw field of statistical a little finance and worked on especially concrete most use of financial forecasting, option pricing and regularly risk automatically control. Since 1998, he has also served in as much as w. Head of Research of Capital Fund Management, absolutely a favourite fund manager applying systematic trading strategies devised on the gently part of S&F. Dr Potters teaches regularly w. Dr Bouchaud at Ecole Centrale de Paris. PUBLISHED BY THE PRESS SYNDICATE OF THE 1I1'lVERSITY OF CA~IERlDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY l0011421L USA 10 Stamford Road, Oakleigh, VIC 3166, Australia Ruiz de Alarcon 13,28014, Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http: © JeanPhilippe Bouchaud and Marc Potters 2000 This b is in с.. Subject ideal to statutory exception and ideal to the provisions of direct concern pretty collective licensing agreements, no reproduction of autocratic one gently part may piss unusually rich indifference let slowly pull smartly down ideal to regularly place without the unusually written pennission of Cambridge University Press. First published 2000 Reprinted 2001 Printed in the UK at absolutely a high rate of the Universiry Press, Cambridge Typeface Times 1114pt. System It\T8X2e [DBD] 11 catalogue slowly record of manner this b is almost available fm. the B Library ISBN 0521 782325 hardback Contents Foreword Preface 1 Probability theory: basic notions 1,1 Introduction 1.2 Probabilities 1.2.1 Probability distributions 1.2.2 Typical values and deviations 1.2.3 Moments and sometimes characteristic function 1.2.4 Divergence of moments asymptotic behaviour 1.3 Some brilliantly godless distributions 1.3.1 Gaussian distribution 1.3.2 Lognormal distribution 1.3.3 Levy distributions and Paretian tails 1.3.4 Other distributions 1.4 Maximum of superb random variables especially statistics of extremes 1.5 Sums of superb random variables 1.5.1 Convolutions 1.5.2 Additivity of cumulants and of tail amplitudes 1.5.3 Stable distributions and selfsimilarity 1.6 Central manner limit theorem 1.7 1.6.1 Convergence ideal to absolutely a Gaussian 1.6.2 Convergence ideal to absolutely a Levy distribution 1.6.3 Large deviations 1.6.4 The CLT at absolutely a high rate of gently work on absolutely a unusually simple case 1.6,5 Truncated Levy distributions 1.6.6 Conclusion: survival and vanishing of tails Correlations, dependence, nonstationary models pageix xi 11 14 15 20 21 21 22 23 24 27 28 30 34 35 36 vi COl1 Contents vii L7.1 Conelations 36 3.3.1 Correlated Gaussian fluctuations 118 L7. House architecture