Evolución de los Métodos Cuantitativos Económico-Financiero-Actuariales.
- Garcia Villalón, Julio
- Rodríguez Ruiz, Julián
- Seijas Macias, José Antonio
ISSN: 2171-892X
Ano de publicación: 2013
Número: 21
Tipo: Artigo
Outras publicacións en: Anales de ASEPUMA
Resumo
The quantitative methods economic-actuarial-financial have experienced a great advance throughout the time. The economists have increasingly met bound to apply by new methods to solve different problems that have been appearing. These problems have been increasingly surfacing. The skill of the economists to raise the problems reflects a body of theory developed well, manners of analyses that emphasize the logic and quantitative sophisticated instruments. The Mathematics and Statistics in the economic-actuarial-financial arena have played a central role in the economic analysis, which has provided a mayor advance in the field, particularly financially, on having allowed the economists to establish rigorously his theorems and to contrasting to empirical validity of his theories. As it refers to the Financial Theory, it has been more than 50 years since it has been simplified to one aspect alone: financial calculation of the actuarial values. At the same time, the financial economists began to use a great variety of increasingly sophisticated mathematical and statistical techniques such as: Probability and optimization Theory, Stochastic calculus, differential stochastic Equation, etc. Well then, in the work that we present here, we cover the evolution of the mathematical technologies and his applications, previously mentioned.
Referencias bibliográficas
- Baxter, M.; Rennie, A (1999). Financial Calculus. Cambridge University Press.
- Cramer, H. (1969). “Historical review of Filip Lundberg’s works on risk theory”. Scandinavian Actuarial Journal, Supplement 3, pp. 6-12.
- Duffie, D. (1996). Dynamic Asset Pricing Theory. Princeton.
- Elliott, R.J.; Kopp, P.E. (2004). Mathematics of Financial Markets. Springer.
- Föllmer, Hans (1981). “Calcul d’Itô sans probabilitiés”. Séminaire de probabilités de Strasbourg, 15, pp. 143-150.
- Föllmer, H.; Schied, A. (2002). Stochastic Finance. De Gruyter.
- Gihman, I.; Skorohold, A. (1974). The Theory of Stochastic Processes, vol. I y II. Springer-Verlag.
- Itô, K. (1944). “Stochastic Integral”. Proceedings of the Imperial Academy, 20 (8), pp. 519-524.
- Itô, K. (1951). “On Stochastic Differential Equations”. Memoires American Mathematical Society, 4, pp: 51.
- Karatzas, I.; Shreve, S.E. (1991). Brownian Motion and Stochastic Calculus. Springer
- Martinez Barbeito, J.; G. Villalon, J. (2003). Introducción al Cálculo Estocástico. Aplicado a la Modelación Económico-Financiero-Actuarial. Netbiblo.
- Norberg, R. (1995). “Stochastic Calculus in Actuarial Science”. Industrial and Applied Mathematics, 2 (5), pp. 1-23.
- Oskendal, B. (1992). Stochastic Differential Equations. Springer.
- Protter, P. (1990). Stochastic Integration and Differential Equations. Springer.
- Revuz, D.; Yor, M. (1994). Continuous Martingales and Brownian Motion. Springer.
- Wilmott, P., Howison, S.; Dewynne, J. (1995). The Mathematics of Financial Derivatives. Cambridge University Press.
- Wilmott, P. (1999). The Theory and Practice of Financial Engineering. Wiley.