Lie symmetry analysis of differential equations in finance
Lie symmetry analysis of differential equations in finance
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DOI：
10.1023/a:1008304132308
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发表时间：
1998-12-01
影响因子：
5.6
通讯作者：
Ibragimov, NH
中科院分区：
文献类型：
--
作者：
Gazizov, RK;Ibragimov, NH
李群理论被应用于在金融问题中作为数学模型出现的微分方程。我们从一维Black-Scholes模型的完全对称性分析入手，证明了该方程包含在Sopus Lie的两个自变量的二阶线性偏微分方程组的分类中。因此，该模型到热传导方程的Black-Scholes变换直接由Lie等价变换公式推导而来。然后根据二维Jacobs-Jones模型方程的对称群对其进行了分类。这种分类为构造精确(不变)解提供了理论背景，并给出了实例。
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.