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**Group classification for a general nonlinear model of option pricing.**
*(English)*
Zbl 1398.91584

Summary: We consider a family of equations with two free functional parameters containing the classical Black-Scholes model, Schonbucher-Wilmott model, Sircar-Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications’ parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.

### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |

### Keywords:

nonlinear partial differential equation; group analysis; group of equivalency transformations; group classiffcation; nonlinear Black-Scholes equation; pricing options; dynamic hedging; feedback effects of hedging
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\textit{V. E. Fedorov} and \textit{M. M. Dyshaev}, Ural Math. J. 2, No. 2, 37--44 (2016; Zbl 1398.91584)

### References:

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