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Abstract:

We study by topological methods a nonlinear differential equation generalizing the Black-Scholes formula for an option pricing model with stochastic volatility. We prove the existence of at least a solution of the stationary Dirichlet problem applying an upper and lower solutions method. Moreover, we construct a solution by an iterative procedure. © 2002 Elsevier Science (USA). All rights reserved.

Registro:

Documento: Artículo
Título:Solutions to a stationary nonlinear Black-Scholes type equation
Autor:Amster, P.; Averbuj, C.G.; Mariani, M.C.
Filiación:Dpto. de Matemática, Fac. de Cs. Exactas y Naturales, UBA Pab. I, Ciudad Universitaria 1428 Capital, Argentina
Año:2002
Volumen:276
Número:1
Página de inicio:231
Página de fin:238
DOI: http://dx.doi.org/10.1016/S0022-247X(02)00434-1
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v276_n1_p231_Amster.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v276_n1_p231_Amster

Referencias:

  • Avellaneda, M., Quantitative Modeling of Derivative Securities (2000), Chapman & Hall/CRC; Amster, P., Mariani, M.C., Sabia, J., A boundary value problem for a semilinear second order ODE (2000) Rev. Un. Mat. Argentina, 41, pp. 61-68
  • Avellaneda, M., Zhu, Y., Risk neutral stochastic volatility model (1998) Internat. J. Theor. Appl. Finance, 1, pp. 289-310
  • Duffie, D., Dynamic Asset Pricing Theory (1996), Princeton University Press; Gilbarg, D., Trudinger, N.S., Elliptic Partial Differential Equations of Second Order (1983), Springer-Verlag; Hull, J.C., Options, Futures, and Other Derivatives (1997), Prentice-Hall; Ikeda, S., Watanabe, S., Stochastic Differential Equations and Diffusion Processes (1989), North-Holland; Jarrow, R.A., Modelling Fixed Income Securities and Interest Rate Options (1997), McGraw-Hill; Merton, R.C., Continuous-Time Finance (2000), Blackwell, Cambridge

Citas:

---------- APA ----------
Amster, P., Averbuj, C.G. & Mariani, M.C. (2002) . Solutions to a stationary nonlinear Black-Scholes type equation. Journal of Mathematical Analysis and Applications, 276(1), 231-238.
http://dx.doi.org/10.1016/S0022-247X(02)00434-1
---------- CHICAGO ----------
Amster, P., Averbuj, C.G., Mariani, M.C. "Solutions to a stationary nonlinear Black-Scholes type equation" . Journal of Mathematical Analysis and Applications 276, no. 1 (2002) : 231-238.
http://dx.doi.org/10.1016/S0022-247X(02)00434-1
---------- MLA ----------
Amster, P., Averbuj, C.G., Mariani, M.C. "Solutions to a stationary nonlinear Black-Scholes type equation" . Journal of Mathematical Analysis and Applications, vol. 276, no. 1, 2002, pp. 231-238.
http://dx.doi.org/10.1016/S0022-247X(02)00434-1
---------- VANCOUVER ----------
Amster, P., Averbuj, C.G., Mariani, M.C. Solutions to a stationary nonlinear Black-Scholes type equation. J. Math. Anal. Appl. 2002;276(1):231-238.
http://dx.doi.org/10.1016/S0022-247X(02)00434-1