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Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance

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  • Khalique, Chaudry Masood
  • Motsepa, Tanki

Abstract

The one-factor term structure model by Vasicek is analysed from the point of view of Lie symmetry analysis. Its one-parameter Lie point symmetries and corresponding group of adjoint representations are obtained. An optimal system of one-dimensional subalgebras is derived and is then used to obtain symmetry reductions and group-invariant solutions. The group-invariant solutions presented here are new and have not appeared in the literature. Moreover, we derive conservation laws for the Vasicek equation by employing the theorem due to Ibragimov.

Suggested Citation

  • Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:871-879
    DOI: 10.1016/j.physa.2018.03.053
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    References listed on IDEAS

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