Algunas aplicaciones de la Teoría de Lie a la Economía y las Finanzas

  1. Hernández Fernández, Isabel
  2. Mateos Contreras, Consuelo
  3. Núñez-Valdés, Juan
  4. Tenorio Villalón, Ángel Francisco
Journal:
Revista de métodos cuantitativos para la economía y la empresa

ISSN: 1886-516X

Year of publication: 2008

Volume: 6

Pages: 74-94

Type: Article

More publications in: Revista de métodos cuantitativos para la economía y la empresa

Abstract

This paper shows and explains two problems in Economics and Finance, both dealt with a Lie Theory approach. So, mathematical aspects for these approaches are put forward and discussed in several economic problems which have been previously considered in the literature. Besides, some ad- vances on this topic are also shown, mentioning some open problems for future research.

Bibliographic References

  • M. Armstrong (1996): Multiproduct Nonlinear Pricing. Econometrica 64, pp. 51-75.
  • S. Basov (2004): Lie groups of partial differential equations and their application to the multidimensional screening problems. Econometric Society 2004 Australasian Meetings 44.
  • T. Björk (2001): A geometric view of interest rate theory. En: E. Jouni, J. Cvitanic and M. Musuela (eds.): Option pricing, Interest Rates and Risk Management, Cambridge University Press, pp. 241-277.
  • T. Björk (2004): On the Geometry of Interest Rate Models. En: R.A. Carmona, E.C. Çinlar, I. Ekeland, E. Jouini, J. A. Scheinkman and N. Touzi (eds.): Paris-Princeton Lectures on Mathematical Finance 2003, Springer-Verlag, pp. 133-216.
  • T. Björk and C. Landén (2002): On the construction of finite dimensional realizations for nonlinear forward rate models. Fin. Stoch. 6, pp. 303-331.
  • J. Cox (1975): Notes on Option Pricing I: Constant Elasticity of Variance Diffusions. Working Paper, Stanford University.
  • J.C. Cox and S.A. Ross (1976): The Valuation of Options for Alternative Stochastic Processes. Journal of Financial Economics 3, pp. 145-166.
  • A. De Sanctis (2007): Lie Theory to Value Financial Derivatives with Time Dependent Parameters. Int. Math. Forum 2:10, pp. 499-503.
  • L.P. Eisenhart (1933): Continuous groups of transformations, Princeton University Press. E.M. Fedriani y Á.F. Tenorio (2006): Progreso técnico: una aproximación desde la Teoría de Grupos de Transformaciones de Lie. Revista de Métodos Cuantitativos para la Economía y la Empresa 1, pp. 5-24.
  • A. Friedman (1964): Partial Differential Equations of Parabolic Type, Prentice-Hall.
  • R.M. Gaspar (2006): Finite Dimensional Markovian Realizations for Forward Price Term Structure Models. En: A.N. Shiryaev, M.R. Grossinho, P.E. Oliveira and M.L. Esquível (eds.): Stochastic Finance, Springer, pp. 265-320.
  • I. Hernández, C. Mateos, J. Núñez and A.F. Tenorio (2008): Lie Theory: Applications to Problems in Mathematical Finance and Economics. Applied Mathematics and Computation. To appear.
  • I. Karatsas and S. Shreve (1997): Brownian Motion and Stochastic Calculus, Springer-Verlag.
  • C.F. Lo, C.H. Hui and P.H. Yuen (2000a): Constant elasticity of variance option pricing model with time-dependent parameters. Int. J. Theor. Appl. Fin. 3:4, pp. 661-674.
  • C.F. Lo, C.H. Hui and P.H. Yuen (2000b): Option risk measurement with time-dependent parameters. Int. J. Theor. Appl. Fin. 3:3, pp. 581-589.
  • C.F. Lo and C.H. Hui (2001): Valuation of financial derivatives with time-dependent parameters. Quantitative Finance 1, pp. 73-78.
  • C.F. Lo and C.H. Lui (2002): Pricing multi-asset financial derivatives with time-dependent parameters-Lie algebraic approach. Int. J. Math. Math. Sci. 32:7, pp. 401-410.
  • C.F. Lo and C.H. Lui (2006): Lie algebraic approach for pricing moving barrier options with time-dependent parameters, J. Math. Ann. Appl. 323:2, pp. 1455-1464.
  • R. Lu and Y.-H. Hsu (2005): Valuation of Standard Options under the Constant Elasticity of Variance Model, Int. J. Bus. Econ. 4:2, pp. 157-165.
  • T.M. Mitchell (1987): Toward empirical applications of Lie-group technical progress functions, Economics Letters 25, pp. 111-116.
  • S. Polidoro (2003): A Nonlinear PDE in Mathematical Finance. En: F. Brezzi, A. Buffa, S. Corsaro and A. Murli (eds.): Numerical Mathematics and Advanced Application, Springer, pp. 429-433.
  • R. Sato (1980): The impact of technical change on the holotheticity of production functions. Economic Studies 47, pp. 767-776.
  • R. Sato (1981): Theory of technical change and economic invariance. Application of Lie groups, Academic Press.
  • R. Sato and R.V. Ramachandran (1998): Symmetry and Economic Invariance: an introduction, Kluwer.
  • R.M. Solow (1961): Comment on Stigler. En: Output, Input and Productivity Measurement, Princeton University Press, pp. 64-68.
  • G.J. Stigler (1961): Economic problems in measuring changes in productivity. En: Output, Input and Productivity Measurement, Princeton University Press, pp. 47-63.
  • J. Wei and E. Norman (1963): Lie algebraic solution of linear differential equations. Journal of Mathematical Physics 4, pp. 575-581.
  • R. Wilson (1993): Non Linear Pricing, Oxford University Press.