Geodesic
Invariant solutions and linearized invariant submodels of some option pricing equations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 3, pp. 446-470

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Some subalgebras of the Lie algebra obtained earlier in the group classification of the option pricing model, taking into account costs and market influence, are considered. For a five-dimensional Lie algebra, invariant submodels are found in the case of one-dimensional subalgebras and invariant solutions are derived in the case of two-dimensional subalgebras of a general type. For three six-dimensional Lie algebras, one-dimensional and two-dimensional subalgebras are considered and exact solutions for a number of linearized invariant submodels are obtained.
Keywords: Black — Scholes type equation, group analysis, admissible group, Lie algebra, invariant submodel, invariant solution. 
@article{CHFMJ_2024_9_3_a6,
     author = {Kh. V. Yadrikhinskiy},
     title = {Invariant solutions and linearized invariant submodels of some  option pricing  equations},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {446--470},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_3_a6/}
}
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Kh. V. Yadrikhinskiy. Invariant solutions and linearized invariant submodels of some  option pricing  equations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 3, pp. 446-470. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_3_a6/