An early political election problem

Under the democratic systems of government instilled in many sovereign states, the party in government maintains a constitutional right to call an early election. Whereas the constitution states that there is a maximum period between elections, early elections are frequently called. This right to call an early election gives the government a control to maximize its remaining period in power. We find the optimal control for the government by locating an exercise boundary, which indicates whether or not a premature election should be called. This problem draws upon the methods of optimal stopping and stochastic control