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A Continuous Time Model for Election Timing

We consider a continuous time model for election timing in a Majoritarian Parliamentary System where the government maintains a constitutional right to call an early election. 
Our model is based on the two-party-preferred data that measure the popularity of the government and the opposition over time. We describe the poll process by a Stochastic 
Diﬀerential Equation (SDE) and use a martingale approach to derive a Partial Diﬀerential Equation (PDE) for the government’s expected remaining life in oﬃce. A comparison 
is made between a three-year and a four-year maximum term and we also provide the exercise boundary for calling an election. Impacts on changes in parameters in the SDE, the probability of winning the election and maximum terms on the call exercise boundaries are discussed and analysed. An application of our model to the Australian Federal Election for House of Representatives is also given.