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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.
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"Black F. S. (1976) The Pricing of Commodity Contracts. Journal of Financial Economics, 3(1-2), 167-179. (Crossref)
Black F.S., Scholes M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. (Crossref)
Bluman G. W., Kumei S. (1989) Symmetries and Differential Equations. Springer, New York. (Crossref)
Bordag L. A. (2015) Geometrical Properties of Differential Equations: Applications of the Lie Group Analysis in Financial Mathematics. World Scientific, Singapore. (Crossref)
Fushchych W. I., Nikitin A. G. (1987) Symmetries of Maxwell’s Equations. Springer, Berlin. (Crossref)
Gazizov R. K., Ibragimov N. H. (1998) Lie Symmetry Analysis of Differential Equations in Finance. Nonlinear Dynamics, 17, 387-407, https://doi.org/10.1023/A:1008304132308. (Crossref)
Harper J. (1994) Reducing Parabolic Partial Differential Equations to Canonical Form. European Journal of Applied Mathematics, 5, 159-164. (Crossref)
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). (Crossref)
Merton R. C. (1971) Optimum Consumption and Portfolio Rules in a Continuous Time Model. Journal of Economic Theory, 3(4), 373‐413. (Crossref)
Merton R. C. (1973) Theory of Rational Option Pricing. Bell Journal of Economics, 4(1), 141‐183. (Crossref)
Miller W. Jr (1984) Symmetry and Separation of Variables. Cambridge University Press. (Crossref)
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. (Crossref)
Olver P. J. (1986) Applications of Lie Groups to Differential Equations. Springer, New York. (Crossref)
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. (Crossref)
Stephani H. (1990) Differential Equations: Their Solution Using Symmetries. Cambridge University Press. (Crossref)
Wilmott P, Howison S., Dewynne J. (1999) The Mathematics of Financial Derivatives. Cambridge University Press."
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