The Lie symmetry approach on (1+2)-dimensional financial models

Linearization in Financial Mathematics

“…The corresponding result for µ = −1 can be found in [3]. Furthermore, for certain forms of the functions f (x), h(x) and k(x) the above nonlinear equation can be transformed into the linear heat equation u t = u xx [3]. Such example, where a nonlinear equation is mapped into the linear heat equation, is given in [4].…”

“…Furthermore, the above two nonlinear equations can be reduced to linear or linearizable ordinary differential equations using Lie symmetry methods [17]. Applications of Lie symmetries on equations of the general class (2) can be found in recent works [3,18]. The financial models are subject to terminal conditions of the form u(t = T, x) = f (x).…”