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Paper No. 11-05

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SD Jacka, J Warren and P Windridge

Minimising the time to a decision

Abstract: Suppose we have three independent copies of a regular diffusion on [0,1] with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimising the total time spent running the processes. Primary MSC classification: 93E20 Optimal stochastic control, Secondary MSC classification: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.),

Keywords: optimal stochastic control, dynamic resource allocation, multiparameter processes, continuous bandits, recursive majority of three.