  We discuss local and global existence and uniqueness for the price formation
free boundary model with homogeneous Neumann boundary conditions introduced by
Lasry & Lions in 2007. The results are based on a transformation of the problem
to the heat equation with nonstandard boundary conditions. The free boundary
becomes the zero level set of the solution of the heat equation. The
transformation allows us to construct an explicit solution and discuss the
behavior of the free boundary. Global existence can be verified under certain
conditions on the free boundary and examples of non-existence are given.
