  Motivated by applications in economics and finance, in particular to the
modeling of limit order books, we study a class of stochastic second-order PDEs
with non-linear Stefan-type boundary interaction. To solve the equation we
transform the problem from a moving boundary problem into a stochastic
evolution equation with fixed boundary conditions. Using results from
interpolation theory we obtain existence and uniqueness of local strong
solutions, extending results of Kim, Zheng and Sowers. In addition, we
formulate conditions for existence of global solutions and provide a refined
analysis of possible blow-up behavior in finite time.
