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We discuss local and global existence and uniqueness for the price formationfree boundary model with homogeneous Neumann boundary conditions introduced byLasry & Lions in 2007. The results are based on a transformation of the problemto the heat equation with nonstandard boundary conditions. The free boundarybecomes the zero level set of the solution of the heat equation. Thetransformation allows us to construct an explicit solution and discuss thebehavior of the free boundary. Global existence can be verified under certainconditions on the free boundary and examples of non-existence are given.

On a price formation free boundary model by Lasry & Lions: The Neumann problem