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On the Mabinogion urn model. (English) Zbl 1431.93065

Summary: In this paper we discuss the Mabinogion urn model introduced by D. Williams [Probability with martingales. Cambridge etc.: Cambridge University Press (1991; Zbl 0722.60001)]. Therein he describes an optimal control problem where the objective is to maximize the expected final number of objects of one kind in the Mabinogion urn model. Our main contribution is formulae for the expected time to absorption and its asymptotic behaviour in the optimally controlled process. We also present results for the noncontrolled Mabinogion urn process and briefly analyze other strategies that become superior if a certain discount factor is included.

MSC:

93E20 Optimal stochastic control
60C05 Combinatorial probability
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
49J21 Existence theories for optimal control problems involving relations other than differential equations
60G50 Sums of independent random variables; random walks

Citations:

Zbl 0722.60001

References:

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