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Optimal halting policies in Markov population decision chains with constant risk posture

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  • Pelin Canbolat

Abstract

This paper concerns infinite-horizon Markov population decision chains with finite state-action space, where one exerts control on a population of individuals in different states by assigning an action to each individual in the system in each period. In every transition, each individual earns a random reward and generates a random progeny vector. The objective of the decision maker is to maximize expected (infinite-horizon) system utility under the following assumptions: (i) The utility function exhibits constant risk posture, (ii) the (random) progeny vectors of distinct individuals are independent, and (iii) the progeny vectors of individuals in a state who take the same action are identically distributed. The paper deals with the problem of finding an optimal stationary halting policy and shows that this problem can be solved efficiently using successive approximations with the original state-action space without enlarging it to include information about the population in each state or any other aspect of the system history in a state. The proposed algorithm terminates after a finite number of iterations with an optimal stationary halting policy or with proof of nonexistence. Copyright Springer Science+Business Media New York 2014

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  • Pelin Canbolat, 2014. "Optimal halting policies in Markov population decision chains with constant risk posture," Annals of Operations Research, Springer, vol. 222(1), pages 227-237, November.
    • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:227-237:10.1007/s10479-012-1302-3
    DOI: 10.1007/s10479-012-1302-3
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    References listed on IDEAS

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    1. Rothblum, Uriel G., 1975. "Multivariate constant risk posture," Journal of Economic Theory, Elsevier, vol. 10(3), pages 309-332, June.
    2. Uriel G. Rothblum, 1984. "Multiplicative Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 6-24, February.
    3. Eric V. Denardo & Haechurl Park & Uriel G. Rothblum, 2007. "Risk-Sensitive and Risk-Neutral Multiarmed Bandits," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 374-394, May.
    4. Ranel E. Erickson, 1988. "Optimality of Stationary Halting Policies and Finite Termination of Successive Approximations," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 90-98, February.
    5. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.
    6. Ronald A. Howard, 1971. "Proximal Decision Analysis," Management Science, INFORMS, vol. 17(9), pages 507-541, May.
    7. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
    8. Giri, B.C., 2011. "Managing inventory with two suppliers under yield uncertainty and risk aversion," International Journal of Production Economics, Elsevier, vol. 133(1), pages 80-85, September.
    9. Choi, Sungyong & Ruszczynski, Andrzej, 2011. "A multi-product risk-averse newsvendor with exponential utility function," European Journal of Operational Research, Elsevier, vol. 214(1), pages 78-84, October.
    10. Eric V. Denardo & Uriel G. Rothblum & Ludo Van der Heyden, 2004. "Index Policies for Stochastic Search in a Forest with an Application to R&D Project Management," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 162-181, February.
    11. Rolando Cavazos-Cadena & Raúl Montes-de-Oca, 2003. "The Value Iteration Algorithm in Risk-Sensitive Average Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 752-776, November.
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    Cited by:

    1. Amanda M. White & Pelin G. Canbolat, 2018. "Finite‐horizon Markov population decision chains with constant risk posture," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 580-593, December.
    2. Rolando Cavazos-Cadena, 2018. "Characterization of the Optimal Risk-Sensitive Average Cost in Denumerable Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 1025-1050, August.

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