Closed-form solutions via the invariant approach for one-factor commodity models

Abstract

We utilise the invariant method for scalar linear (1+1) parabolic partial differential equations so as to effect reductions via invertible transformations to Lie canonical forms of the first and third types. This is performed for the one-factor commodity models that have parameters which are constants or dependent on the price of stock or the time. The unknown parameters of the equations are determined. New closed-form solutions for the simple transformed equations are deduced by utilizing the equivalence maps and known solutions of the two Lie canonical forms.