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2021 | 22(XXII) | nr 2 | 77--86
Tytuł artykułu

Symmetry Properties of Modified Black-Scholes Equation

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper concerns the classical and conditional symmetries of the Black-Scholes equation. Modifications of the Black-Scholes equation have also been considered and their maximal algebras of invariance have been found. Examples of creation operators for the Black-Scholes eigenvalue problem have been provided.(original abstract)
Twórcy
  • Warsaw University of Life Sciences - SGGW, Poland
  • Warsaw University of Life Sciences - SGGW, Poland
Bibliografia
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  • Bluman G. W., Kumei S. (1989) Symmetries and Differential Equations. Springer, New York.
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  • Harper J. (1994) Reducing Parabolic Partial Differential Equations to Canonical Form. European Journal of Applied Mathematics, 5, 159-164.
  • Lyu W., Wang Y. (2017) Black-Scholes Equation with the Variable Risk-free Interest Rate. 2nd International Conference on Advances in Management Engineering and Information Technology (AMEIT 2017).
  • Merton R. C. (1971) Optimum Consumption and Portfolio Rules in a Continuous Time Model. Journal of Economic Theory, 3(4), 373-413.
  • Merton R. C. (1973) Theory of Rational Option Pricing. Bell Journal of Economics, 4(1), 141-183.
  • Miller W. Jr (1984) Symmetry and Separation of Variables. Cambridge University Press.
  • Naz R., Naeem I. (2020) Exact Solutions of a Black-Scholes Model with Time-Dependent Parameters by Utilizing Potential Symmetries. Discrete and Continuous Dynamical Systems, Series S, 13(10), 2841-2851.
  • Olver P. J. (1986) Applications of Lie Groups to Differential Equations. Springer, New York.
  • Ovsyannikov L. V. (1962) Group Properties of Differential Equations. USSR Academy of Sciences, Siberian Branch, Novosibirsk [in Russian].
  • Rodrigo M.R., Mamon R.S. (2006) An alternative approach to solving the Black-Scholes equation with time-varying parameters. Applied Mathematics Letters 19(4), 398-402.
  • Stephani H. (1990) Differential Equations: Their Solution Using Symmetries. Cambridge University Press.
  • Wilmott P, Howison S., Dewynne J. (1999) The Mathematics of Financial Derivatives. Cambridge University Press.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.ekon-element-000171652970

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