Lie Symmetry Reductions and Exact Solutions of an Option-Pricing Equation for Large Agents

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• 作者：Senkepeng Louisa Lekalakala ; Tanki Motsepa…
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：13
• 期：4
• 页码：1753-1763
• 全文大小：494 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this paper, we study a nonlinear partial differential equation that models the one-factor term structure option-pricing for large agents from the Lie symmetry stand point. This equation was modelled by Jonsson and Keppo (Appl Math Financ 9:261–272, 2002) and is a nonlinear modified Black–Scholes partial differential equation. We first determine an optimal system of one-dimensional subalgebras. We then use it to obtain symmetry reductions and families of group-invariant solutions of the underlying equation.Mathematics Subject Classification35A0935C0535C0676M60