Symmetry classification and invariant solutions of the classical geometric mean reversion process
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912333110968320 |
|---|---|
| author | Zhang, Jin Gao, Dapeng |
| author_facet | Zhang, Jin Gao, Dapeng |
| contents | Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries and the corresponding one-parameter symmetry groups of the equation are obtained. An optimal system of invariant solutions are constructed by a derived optimal system of one-dimensional subalgebras. Because of taking into account a supply response to price rises, this equation provides for a more realistic assumption than the geometric Brownian motion in many investment scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry classification and invariant solutions of the classical geometric mean reversion process Zhang, Jin Gao, Dapeng Dynamical Systems Analysis of PDEs Probability Mathematical Finance Based on the Lie symmetry method, we investigate a Feynman-Kac formula for the classical geometric mean reversion process, which effectively describing the dynamics of short-term interest rates. The Lie algebra of infinitesimal symmetries and the corresponding one-parameter symmetry groups of the equation are obtained. An optimal system of invariant solutions are constructed by a derived optimal system of one-dimensional subalgebras. Because of taking into account a supply response to price rises, this equation provides for a more realistic assumption than the geometric Brownian motion in many investment scenarios. |
| title | Symmetry classification and invariant solutions of the classical geometric mean reversion process |
| topic | Dynamical Systems Analysis of PDEs Probability Mathematical Finance |
| url | https://arxiv.org/abs/2504.13094 |