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Abstract:

We study an integro-differential parabolic problem arising in Financial Mathematics. Under suitable conditions, we prove the existence of solutions for a multi-asset case in a general domain using the method of upper and lower solutions and a diagonal argument. We also model the jump in the related integro differential equation and give a solution procedure for that model assuming that the brownian motions are not correlated. For a bounded domain, this model for the jump gives an elegant expression of the solution in terms of hyper-spherical harmonics. © 2012 Springer Science+Business Media B.V.

Registro:

Documento: Artículo
Título:Solutions to integro-differential problems arising on pricing options in a Lévy market
Autor:Sengupta, I.; Mariani, M.C.; Amster, P.
Filiación:Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, United States
Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Financial market; Integro-differential operator; Levy model; Spherical harmonics; Upper and lower solutions; Financial market; Integro-differential operator; Levy model; Spherical harmonics; Upper and lower solutions; Brownian movement; Differential equations; Mathematical operators; Harmonic analysis
Año:2012
Volumen:118
Número:1
Página de inicio:237
Página de fin:249
DOI: http://dx.doi.org/10.1007/s10440-012-9687-1
Título revista:Acta Applicandae Mathematicae
Título revista abreviado:Acta Appl Math
ISSN:01678019
CODEN:AAMAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01678019_v118_n1_p237_Sengupta

Referencias:

  • Adams, R., (1975) Sobolev Spaces, , Academic Press San Diego 0314.46030
  • Amster, P., Averbuj, C.G., Mariani, M.C., Solutions to a stationary nonlinear Black-Scholes type equation (2002) Journal of Mathematical Analysis and Applications, 276 (1), pp. 231-238. , DOI 10.1016/S0022-247X(02)00434-1, PII S0022247X02004341
  • Andersen, L., Andreasen, J., Jumps diffusion models: Volatility smile fitting and numerical methods for pricing (2000) Rev. Deriv. Res., 4, pp. 231-262. , 10.1023/A:1011354913068
  • Avellaneda, M., Zhu, Y., Risk neutral stochastic volatility model (1998) Int. J. Theor. Appl. Finance, 1 (2), pp. 289-310. , 0909.90036 10.1142/S0219024998000163
  • Bebernes, J.W., Schmitt, K., On the existence of maximal and minimal solutions for parabolic partial differential equations (1979) Proc. Am. Math. Soc., 73 (2), pp. 211-218. , 516467 0399.35065 10.1090/S0002-9939-1979-0516467-3
  • Berestycki, H., Busca, J., Florent, I., Computing the implied volatility in stochastic volatility models (2004) Communications on Pure and Applied Mathematics, 57 (10), pp. 1352-1373. , DOI 10.1002/cpa.20039
  • Black, F., Scholes, M., The pricing of options and corporate liabilities (1973) J. Polit. Econ., 81, pp. 637-659. , 10.1086/260062
  • Cont, R., Tankov, P., (2003) Financial Modeling with Jumps Processes, , Chapman & Hall/CRC Press London/Boca Raton 10.1201/9780203485217
  • Duffie, D., (1996) Dynamic Asset Pricing Theory, , Princeton University Press Princeton
  • Dehghan, M., Shakeri, F., Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method (2008) Prog. Electromagn. Res., 78, pp. 361-376. , 10.2528/PIER07090403
  • Dugundji, J., An extension of Tietze's theorem (1951) Pac. J. Math., 1, pp. 353-367. , 44116 0043.38105
  • Geman, H., Pure jump Lévy processes for asset price modeling (2002) J. Bank. Finance, 26, pp. 1297-1316. , 10.1016/S0378-4266(02)00264-9
  • He, J.H., Homotopy perturbation technique (1999) Comput. Methods Appl. Mech. Eng., 178, pp. 257-262. , 0956.70017 10.1016/S0045-7825(99)00018-3
  • Heston, S., A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993) Rev. Financ. Stud., 6, p. 327. , 10.1093/rfs/6.2.327
  • Hull, J.C., (1997) Options, Futures, and Other Derivatives, , Prentice Hall New York
  • Ikeda, N., Watanabe, S., (1989) Stochastic Differential Equations and Diffusion Processes, , North-Holland Amsterdam 0684.60040
  • Jarrow, R., (1997) Modelling Fixed Income Securities and Interest Rate Options, , McGraw-Hill New York
  • Krylov, N., (1996) Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Math., 12. , AMS Providence 0865.35001
  • Lieberman, G., (1996) Second Order Parabolic Differential Equations, , World Scientific Singapore 0884.35001
  • Merton, R., (2000) Continuous-Time Finance, , Blackwell Cambridge
  • Sengupta, I., Differential operator related to the generalized superradiance integral equation (2010) J. Math. Anal. Appl., 369, pp. 101-111. , 2643850 1190.47091 10.1016/j.jmaa.2010.02.034

Citas:

---------- APA ----------
Sengupta, I., Mariani, M.C. & Amster, P. (2012) . Solutions to integro-differential problems arising on pricing options in a Lévy market. Acta Applicandae Mathematicae, 118(1), 237-249.
http://dx.doi.org/10.1007/s10440-012-9687-1
---------- CHICAGO ----------
Sengupta, I., Mariani, M.C., Amster, P. "Solutions to integro-differential problems arising on pricing options in a Lévy market" . Acta Applicandae Mathematicae 118, no. 1 (2012) : 237-249.
http://dx.doi.org/10.1007/s10440-012-9687-1
---------- MLA ----------
Sengupta, I., Mariani, M.C., Amster, P. "Solutions to integro-differential problems arising on pricing options in a Lévy market" . Acta Applicandae Mathematicae, vol. 118, no. 1, 2012, pp. 237-249.
http://dx.doi.org/10.1007/s10440-012-9687-1
---------- VANCOUVER ----------
Sengupta, I., Mariani, M.C., Amster, P. Solutions to integro-differential problems arising on pricing options in a Lévy market. Acta Appl Math. 2012;118(1):237-249.
http://dx.doi.org/10.1007/s10440-012-9687-1