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Fractals and Scaling in Finance by Benoit B. Mandelbrot
  • Fractals and Scaling in Finance

  • Discontinuity, Concentration, Risk

  • by Benoit Mandelbrot
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    Description of Fractals and Scaling in Finance

    This is the first book in the Selecta, the collected works of Benoit Mandelbrot. This volume incorporates his original contributions to finance and is a major contribution to the understanding of how speculative prices vary in time. The chapters consist of much new material prepared for this volume, as well as reprints of his classic papers. Much of this work helps to lay a foundation for evaluating risks in trading strategies. Statistical Papers, 2000: "...this is a most useful collection of Mandelbrot's work economics, it provides an excellent starting point for anybody interested in the origin of many current topics in empirical finance or the distribution of income."

    Reviews

    'Benoit Mandelbrot has been an incorrigibly original mind, an economists have been blessed by his insights. On the scroll of great non-economists who have advanced economics by quantum leaps, next to John von Neumann we read the name of Benoit Mandelbrot.'
    Paul A Samuelson, MIT, Nobel Economist

    Contents of Fractals and Scaling in Finance

    Part One - Nonmathematical Presentations

    1. Introduction
    2. Discontinuity and scaling: scope and likely limitations
    3. New methods in statistical economics
    4. Sources of inspiration and historical background

    Part Two - Mathematical Presentations

    5. States of randomness from mild to wild, and concentration in the short, medium and long run
    6. Self-similarity and panorama of self-affinity
    7. Rank-size plots, Zipf's law, and scaling
    8. Proportional growth with or without diffusion, and other explanations of scaling
    9. A case against the lognormal distribution

    Part Three - Personal Incomes and Firm Sizes

    10. L-stable model for the distribution of income
    11. L-stability and multiplicative variation of income
    12. Scaling distributions and income maximisation
    13. Industrial concentration and scaling

    Part Four - The M 1963 Model of Price Variation

    14. The variation of certain speculative prices
    15. The variation of the price of cotton, wheat, and railroad stocks, and of some financial rates
    16. Mandelbrot on price variation
    17. Comments by P H Cootner, E Parzen and W S Morris
    18. Computation of the L-stable distributions

    Part Five - Beyond The M 1963 Model

    19. Nonlinear forecasts, rational bubbles, and martingales
    20. Limitations of efficiency and martingales
    21. Self-affine variation in fractal time

    Cumulative Bibliography

    Index


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