A class of non-linear equations of RAPM (risk-adjusted pricing methodology) model type with a free element, depending on the second derivative with respect to the underlying asset, is studied. This class contains the Jandačka–Ševčovič model of the option pricing with taking into account transactions costs. The equivalence transformations continuous group of the equations class is found and is applied to the group classification obtaining for the model. The symmetries of the found free element specifications in the considered model are used for the deriving multi-parameter exact solutions.

中文翻译：

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一类RAPM类型的非线性模型的组分类

研究了一类带有自由元素的RAPM（风险调整定价方法）模型类型的非线性方程，具体取决于基础资产的二阶导数。该类包含考虑交易成本的期权定价的Jandačka–Ševčovič模型。找到方程类的等价变换连续群，并将其应用于模型的群分类获得。在考虑的模型中找到的自由元素规范的对称性用于导出多参数精确解。