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In this paper we introduce a completely continuous and time-variate model ofthe evolution of market limit orders based on the existence, uniqueness, andregularity of the solutions to a type of stochastic partial differentialequations obtained in Zheng and Sowers (2012). In contrary to several modelsproposed and researched in literature, this model provides complete continuityin both time and price inherited from the stochastic PDE, and thus isparticularly suitable for the cases where transactions happen in an extremelyfast pace, such as those delivered by high frequency traders (HFT's).  We first elaborate the precise definition of the model with its associatedparameters, and show its existence and uniqueness from the related mathematicalresults given a fixed set of parameters. Then we statistically derive parameterestimation schemes of the model using maximum likelihood and leastmean-square-errors estimation methods under certain criteria such as AIC toaccommodate to variant number of parameters . Finally as a typical economicsand finance use case of the model we settle the investment optimization problemin both static and dynamic sense by analysing the stochastic (It\^{o})evolution of the utility function of an investor or trader who takes the modeland its parameters as exogenous. Two theorems are proved which provide criteriafor determining the best (limit) price and time point to make the transaction.

A Model of Market Limit Orders By Stochastic PDE's, Parameter Estimation, and Investment Optimization