Lie symmetry analysis for a parabolic Monge-Ampère equation in the optimal investment theory

In this paper, Lie symmetry analysis is performed on the parabolic Monge-Ampère equation usuyy+ryuyuyy−θuy2=0 arising from the optimal investment theory. Lie symmetry and optimal system of this equation are derived. In particular, based on optimal system, symmetry reductions and invariant solutions are obtained.