Research Article

A Longstaff and Schwartz Approach to the Early Election Problem

Table 1

 Step Summary Description 0 Develop initial estimate for the value function (Detail Section 4.6) Establish an estimate for the value function at time across all poll states . 1 Simulation of the poll process(Detail Section 4.2) Generate trajectories of the SDE (4.6) by simulating solutions. Denote each of the N simulated poll process as . 2 Simulation of electoral outcome if calling an election (Detail Section 4.4) At each decision point , and poll state , we establish the expectation of the value function from a decision to call an election. The electoral result arises from:  (i) Continue the diffusion to time    (ii) Simulate a sampling error for the poll state  (iii) Simulate the randomness in relationship in Section 3.3 for the imperfect relationship between nationwide polling and the distribution of seats. 3 Simulation of electoral outcome if not calling an election The alternative to the step 2 is to NOT call an election. In that case, the polls will diffuse to the next timestep and the decision experiment is repeated. 4 Perform regression (Detail Section 4.5) Regress over all N simulations the value function conditioned upon the poll state under the scenario that an election IS called (step 2).Regress over all N simulations the value function conditioned upon the poll state under the scenario that an election IS NOT called (step 3). 5 Establish max and strategy Establish the maximum arising from steps 3 or 4; if 3 then assign the optimal strategy as CALL, else CONTINUE. Assign the value function to each of the points , , from the maximum between the two regressions. 6 Repeat over all timesteps Repeat over all time steps stepping backwards from to . 7 Update initial value estimate When time zero is reached, the value function will disagree with the estimate from step 0. Update with the derived initial value and recommence from step 0 until convergence of the initial estimate is achieved.

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