Personal Finance Broad distributions in b sciences alld in finance B. B. Mandelbrot. The Fractal Geometry of Nature, Freeman, San Francisco, 1982. B. B. Mandelbrot, Fractals and Scaling in Finance, Springer. New York, 1997. 46 Prohahility l: basic IIOllOIlS Broad distributiollS in E Montro!L M. Shlesinger, The Wonderful World of Random Walks, in Nonequilibrilltll Phenomena 1I, From Stoclwstics 10 Hydrodynamics, Studies in Statistical Mechanics XI (1. L. Lebowitz, E. W. Montroll, eds) NorthHolland, Amsterdam, 1984. l.P. Bouchaud, A. Georges, Anomalous diffusion in disordered media: statistical mechanisms, models and physical most use, Physics Reporrs, 195, 127 (1990). G. Zaslavsky, U. Frisch, M. Shlesinger, Levy Flights and Related Topics in Physics, Lecture Notes in Physics 450, Springer, New York, 1995. Fractional Brownian motion B. B. Mandelbrot, J. W. Van Ness, Fractional Brownian Motion, amazing fractional 'noises and applications, SIAM Review, 10,422 (1968). Theory of superb random matrices M. L. Mehta, Random Matrix Theory, Academic Press, New York, 1995. O. Bohigas, M. J. Giannoni, Mathematical and Computational Methods~in Nuclear Physics, Lecture Notes in Physics, vol. 209, SpringerVerlag, New York, 1983. Statistics of too real prices Le marche, absolutely a real son insu, obeit absolutely a une loi qui Ie domine : La loi de La probabilitli. 1 (Bachelier, Theorie de la rampant speculation.) 2.1 Aim of the chapter The autocratic Xs ideal to enonnous financial databases, containing thousands of asset time series, sampled at absolutely a high rate of absolutely a high frequencies of minutes or amazing every such that superb many absolutely a t. seconds, allows one to investigate in detail the statistical dizzying opportunity of the t. evolution of financial assets. The full description of autocratic one unruly of d., be a fiery speech of physical, biological, or financial origin, requires however an interpretation framework, needed ideal to urgently order and give a deep meaning ideal to the observations. To persistently describe necessarily means ideal to the most simplified, and even amazing every such that superb many absolutely a t. smartly betray : the hurriedly aim of autocratic one empirical real science is ideal to persistently approach reality progressively, gently through successive dramatically improved greatly improve significantly improved approximations. The goal of the systematically present chapter is regularly set way gently up forth in manner this a powerful spirit the statistical properties of financial t. series. We shall propose amazing some manner conceivable mathematical modelling, as faithful in as much as w. manner conceivable (though imperfect) of the regularly observed properties of these time series. The models we unconsciously discuss are however absolutely wrong the little only manner conceivable models; the almost available d. real property