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Invariance properties of a general bond-pricing equation. (English) Zbl 1147.91017
Summary: We perform the group classification of a bond-pricing partial differential equation of mathematical finance to discover the combinations of arbitrary parameters that allow the partial differential equation to admit a nontrivial symmetry Lie algebra. As a result of the group classification we propose “natural” values for the arbitrary parameters in the partial differential equation, some of which validate the choices of parameters in such classical models as that of Vasicek and Cox-Ingersoll-Ross. For each set of these natural parameter values we compute the admitted Lie point symmetries, identify the corresponding symmetry Lie algebra and solve the partial differential equation.
MSC:
91B24Price theory and market structure
91B28Finance etc. (MSC2000)
35A30Geometric theory for PDE, characteristics, transformations
35K15Second order parabolic equations, initial value problems
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