A free boundary problem arising from a multi-state regime-switching stock trading model

Abstract

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock whose price is driven by unobservable market status and noise processes. The free boundary problem is a variational inequality system of three functions with a degenerate operator. We prove that all the four switching free boundaries are no-overlapping, monotonic and C∞-smooth by the approximation method. We also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.