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De Bachelier a Merton: 100 años del movimiento Browniano en economía y finanzas

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  • Venegas-Martínez, Francisco

    (Escuela Superior de Economía, Instituto Politécnico Nacional)

Abstract

En este trabajo se revisan y discuten las contribuciones de Louis Bachelier, Paul Samuelson, Fisher Black, Myron Scholes y Robert Merton a la economía y las finanzas en tiempo continuo. En sus aportaciones, el movimiento Browniano no sólo permite el modelado adecuado de las fluctuaciones propias de diversas variables económicas y financieras, sino también representa una herramienta básica para incorporar elementos de riesgo e incertidumbre en la dinámica de dichas variables. Asimismo, se discuten relaciones existentes entre dichas aportaciones con las investigaciones de otros prominentes científicos, tales como: Robert Brown, Albert Einstein, Andrey Markov, Andrei Kolmogorov, Paul Lévy, Norbert Wiener y Kiyosi Ito, entre otros. Por último, se lleva a cabo una investigación sobre la evolución de las ideas y formulación de los modelos desarrolldos por Bachelier, Samuelson, Black, Scholes y Merton y, simultaneamente, se realiza un análisis comparativo entre dichos modelos. / This paper is aimed to review and discuss the contributions from Louis Bachelier, Paul Samuelson, Fisher Black, Myron Scholes and Robert Merton to continous-time economics and finance. In their research, the Brownian motion not only provides a suitable modeling of the proper movements of many economic and financial variables, but also it is a very helpful tool to incorporate elements af risk and uncertainty in the dynamic of such variables. Also, the existing relationships between these contributions and the research from other prominent scientist, such as, Robert Brown, Albert Einstein, Andrey Markov, Andrei Kolmogorov, Paul Lévy, Norbert Wiener and Kiyosi Ito, are discussed. Finally, the paper investigates the evolution of the ideas and formulations of the developed models by Bachelier, Samuelson, Black, Scholes, and Merton, and, simultaneously, carries out a comparative analysis among such models.

Suggested Citation

  • Venegas-Martínez, Francisco, 2005. "De Bachelier a Merton: 100 años del movimiento Browniano en economía y finanzas," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(1), pages 9-64, primer se.
    • Handle: RePEc:ipn:panora:v:i:y:2005:i:01:p:09-64
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    Keywords

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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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