We introduce and analyse linear systems of hyperbolic partial differential equations that model the replacement and hoarding of currency. The goal is to deduce the hoarding behavior from observations of circulating bills. The large time asymptotics of the models is identified in all cases. The mathematical analysis is novel, partly because of nonstandard boundary conditions. To identify parameters we suggest the measurement of the age histogram of notes, the rate of growth, and the retard in wear of notes due to hoarding. In our models that suffices to identify all but one quantity.
Quercioli, Elena and Rauch, Jeffrey, Hyperbolic Systems Modeling Currency Hoarding (2010). Volume 8, Number 2 (2010), 70-91, Available at SSRN: https://ssrn.com/abstract=2126107
Commun. Math. Anal.