Group classification for a class of non-linear models of the RAPM type

Fedorov, Vladimir E.; Dyshaev, Mikhail M.

doi:10.1016/j.cnsns.2020.105471

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…In the last decade, in the works of Bordag [24,25], of Dyshaev and Fedorov [26][27][28][29][30][31][32] group properties of various nonlinear Black-Scholes type models were studied, and their invariant solutions and submodels were calculated. In the papers of Dyshaev and Fedorov, group classifications for various classes of nonlinear Black-Scholes type models were obtained.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis of a Model of Option Pricing and Hedging

2022

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The Guéant 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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Section: Introductionmentioning

confidence: 99%

Symmetry Analysis of a Model of Option Pricing and Hedging

2022

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“…The invariants associated with the admitted Lie algebras are deduced and they are utilized for the analysis of the underlying DEs, inter alia, integration and classification. 3 – 11 , 13 , 14 , 12 , 15 , 16 Most of the focus in the literature, is related to regular differential invariants of the corresponding Lie algebras of the DEs under study. Singularity of the differential invariant structure associated with the Lie algebra of the underlying DEs is rather limited and often overlooked.…”

Section: Introductionmentioning

confidence: 99%

Classification of singular differential invariants in (1+3)-dimensional space and integrability

et al. 2021

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Singularity is one of the important features in invariant structures in several physical phenomena reflected often in the associated invariant differential equations. The classification problem for singular differential invariants in (1+3)-dimensional space associated with Lie algebras of dimension 4 is investigated. The formulation of singular invariants for a Lie algebra of dimension [Formula: see text] possessed by the underlying system of three second-order ordinary differential equations is studied in detail and the corresponding canonical forms for these systems are deduced. Furthermore, the categorization of singular invariants on the basis of conditional singularity, weak uncoupling, weak linearization, partial uncoupling and partial linearization are described for the underlying canonical forms. In addition, those cases of classified canonical forms are also mentioned which do not lead to singular invariant systems of three second-order ODEs for a Lie algebra of dimension 4. The integrability aspect of these classified singular-invariant systems in (1+3)-dimensional space is discussed in a detailed manner for a Lie algebra of dimension 4. Finally, two physical systems from mechanics are presented to illustrate the utilization of the physical aspect of these singular invariants.

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