A Betchov-Type Hydrodynamic Formulation of the Ivancevic Option-Pricing Equation

Abstract

We show that, under constant-coefficient assumptions, the Ivancevic option-pricing nonlinear Schrödinger equation admits a Betchov-type hydrodynamic formulation analogous to the one appearing in the context of the vortex filament equation. We identify the corresponding continuity equation and momentum-type conservation law satisfied by the density--velocity pair and illustrate the formulation on known Ivancevic-type soliton solutions. The resulting interpretation is structural and model-dependent, and is intended as a bridge between nonlinear wave formulations in mathematical finance and geometric fluid mechanics.