| Autor: | N. H. Ibragimov, R. K. Gazizov |
|---|---|
| Rok vydání: | 1998 |
| Předmět: |
Finance
Partial differential equation business.industry Differential equation Applied Mathematics Mechanical Engineering Aerospace Engineering Lie group Ocean Engineering Stochastic partial differential equation Examples of differential equations Control and Systems Engineering Ordinary differential equation Lie theory Electrical and Electronic Engineering business Mathematics Separable partial differential equation |
| Zdroj: | Nonlinear Dynamics. 17:387-407 |
| ISSN: | 0924-090X |
| Popis: | Lie group theory is applied to differential equations occurring as mathematical models in financial problems. We begin with the complete symmetry analysis of the one-dimensional Black–Scholes model and show that this equation is included in Sophus Lie's classification of linear second-order partial differential equations with two independent variables. Consequently, the Black–Scholes transformation of this model into the heat transfer equation follows directly from Lie's equivalence transformation formulas. Then we carry out the classification of the two-dimensional Jacobs–Jones model equations according to their symmetry groups. The classification provides a theoretical background for constructing exact (invariant) solutions, examples of which are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink