Abstract
Black–Scholes equation has been widely used by academicians and practitioners. In the classical model, transaction costs are not considered and volatility is assumed to be constant, which is not consistent with practice.
Having the works of Leland (J. Finance 40:1283–1301, 1985) and Avellaneda et al. (Int. J. Theor. Appl. Finance 1:289–310, 1998) in view, we present two results that contribute to the mathematical study of the above questions. We prove the existence of stationary solutions of nonlinear versions of the standard parabolic Black–Scholes PDE, following the framework of Amster et al. (J. Math. Anal. Appl. 276:231–238, 2002; J. Math. Anal. Appl. 303:688–695, 2005), and using the upper and lower solutions method.
Keywords
- Transaction Cost
- Option Price
- Stochastic Volatility Model
- Option Price Model
- Scholes Model
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References
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© 2012 Springer-Verlag Berlin Heidelberg
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de Fátima Fabião, M., do Rosário Grossinho, M., Morais, E., Simões, O.A. (2012). Stationary Solutions of Some Nonlinear Black–Scholes Type Equations Arising in Option Pricing. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry(), vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_26
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DOI: https://doi.org/10.1007/978-3-642-25100-9_26
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