Sobre la aplicacion del "Cálculo Estocastico" en las Matematicas Economico-Financiero-Actuariales

• Villalón, Julio G. ^[3] ; Rodríguez Ruz, Julian ^[1] ; Seijas, J. Antonio ^[2]
  1. [1] Universidad Nacional de Educación a Distancia

     Universidad Nacional de Educación a Distancia

     Madrid, España

     
  2. [2] Universidade da Coruña

     Universidade da Coruña

     A Coruña, España

     
  3. [3] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     

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• Localización: Anales de ASEPUMA, ISSN-e 2171-892X, Nº. 25, 2017
• Idioma: español
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Esta ponencia se ha escrito como una referencia al Calculo Estocastico o Calculo It^o aplicado al campo economico- nanciero-actuarial en dos partes relativas a: Las ma- tematicas economico nancieras y las matematicas actuariales. Por lo que se re ere a la primera parte, tratamos de dar una presentacion moderna de algunos modelos usados en la \Financiera Estocastica" comenzando con el fundamental desarrollo de Black-Scholes y Merton a comienzos de 1970. Con relacion a la Ciencia Actuarial, diremos que mostro rudimentos del \calculo estocastico" hace mas de un siglo con las ecuaciones diferenciales para las reservas de una poliza de seguros obtenidas por Thiele en 1875 y para la pro- babilidad de ruina de una empresa de seguros, Lundberg en 1903, cuando la nocion de \procesos estocasticos" aun no se haba establecido de forma precisa.

  • English

    The attached paper has been written in reference to \stochastic calculus" or \It^o Calculus" applied to the actuarial nance economics relative to two separate sides. The rst is focused on nancial mathematics in economics and we attempt to present a modern look at some of the models use in \stochastic nance" starting with key principles of Black- Scholes and Merton in the early 70's.

    In reference to Actuarial Science o age-continuous actuarial mathematics, we see early signs in the \stochastic calculus" over a century ago in those di erential equations developed for the mathematical reserve of an insurance annuity, rst proposed by Thiele in 1875 and later on for risk or ruin theory for insurance companies proposed by Lundberg in 1903 when stochastic theory had not even been formalized as such.

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