Data assimilation in price formation

Abstract

Abstract We consider the problem of estimating the density of buyers and vendors in a nonlinear parabolic price formation model using measurements of the price and the transaction rate. Our approach is based on a work by Puel (Puel J-P 2002 C. R. Acad. Sci., Paris 335 (2) 161–166), and results in an optimal control problem. We analyze this problems and provide stability estimates for the controls as well as the unknown density in the presence of measurement errors. Our analytic findings are supported with numerical experiments.