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Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes

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Abstract

In this paper we consider a Markov decision model introduced by Economou (2003), in which it was proved that the optimal policy in the problem of controlling a compound immigration process through total catastrophes is of control-limit type. We show that the average cost of a control-limit policy is unimodal as a function of the critical point. This result enables us to design very efficient algorithms for the computation of the optimal policy as the bisection procedure and a special-purpose policy iteration algorithm that operates on the class of control-limit policies.

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Authors and Affiliations

  1. Department of Financial and Management Engineering, University of the Aegean, 31 Fostini Str., 82100, Chios, Greece

    Epaminondas G. Kyriakidis

  2. Department of Statistics and Actuarial Science, University of the Aegean, Karlovassi, 83200, Samos, Greece

    Theodosis D. Dimitrakos

Authors
  1. Epaminondas G. Kyriakidis
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  2. Theodosis D. Dimitrakos
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Correspondence to Epaminondas G. Kyriakidis.

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AMS 2000 Subject Classification: Primary 9OC40; Secondary 6OJ25

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Kyriakidis, E.G., Dimitrakos, T.D. Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes. Methodol Comput Appl Probab 7, 97–118 (2005). https://doi.org/10.1007/s11009-005-6657-3

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  • DOI: https://doi.org/10.1007/s11009-005-6657-3

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