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.

中文翻译：

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价格形成中的数据同化

我们考虑在非线性抛物线价格形成模型中使用价格和交易率的测量来估计买家和卖家的密度的问题。我们的方法基于 Puel 等人的工作，参见 \cite{Puel2002}，并导致最优控制问题。我们分析了这个问题，并在存在测量误差的情况下为控制以及未知密度提供稳定性估计。我们的分析结果得到了数值实验的支持。