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 et al., see cite{Puel2002}, and results in a optimal control problem. We analyse 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.
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