Symmetry Analysis of a Model of Option Pricing and Hedging

被引：5
作者：
Sitnik, Sergey M. [1 ]
Yadrikhinskiy, Khristofor, V [2 ]
Fedorov, Vladimir E. [2 ,3 ]
机构：
[1] Belgorod State Natl Res Univ BelGU, Inst Engn & Digital Technol, Dept Appl Math & Comp Modeling, Pobedy St 85, Belgorod 308015, Russia
[2] North Eastern Fed Univ, Far Eastern Ctr Math Res, Yakut Branch, 58 Belinskiy St, Yakutsk 677000, Russia
[3] Chelyabinsk State Univ, Math Fac, Math Anal Dept, 129 Kashirin Bros St, Chelyabinsk 454001, Russia
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 09期
关键词：
Gueant and Pu model; option pricing; group analysis of differential equations; symmetry analysis; symmetry group; Lie algebra; equivalence transformation; group classification; optimal system of subalgebras; invariant submodel; DIFFERENTIAL-EQUATIONS; PROGRAM;
D O I：
10.3390/sym14091841
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The Gueant and Pu model of option pricing and hedging, which takes into account transaction costs, and the impact of operations on the market is studied by group analysis methods. The infinite-dimensional continuous group of equivalence transforms of the model is found. It is applied to get the group classification of the model under consideration. In addition to the general case, the classification contains three specifications of a free element in the equation, which correspond to models with groups of symmetries of a special kind. Optimal systems of subalgebras for some concrete models from the obtained classification are derived and used for the calculation of according invariant submodels.
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页数：18
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