Advances in Decision Sciences / 2012 / Article / Tab 1

Research Article

A Longstaff and Schwartz Approach to the Early Election Problem

Table 1


0Develop initial estimate for the value function (Detail Section 4.6)Establish an estimate for the value function at time across all poll states .

1Simulation 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 .

2Simulation 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.

3Simulation of electoral outcome if not calling an electionThe 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.

4Perform 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).

5Establish max and strategyEstablish 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.

6Repeat over all timestepsRepeat over all time steps stepping backwards from to .

7Update initial value estimateWhen 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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