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Robust best choice problem

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  • Lazar Obradović

    (Bielefeld University
    University of Montenegro)

Abstract

We consider a robust version of the full information best choice problem: there is model uncertainty, represented by a set of priors, about the measure driving the observed process. We propose a general construction of the set of priors that we use to solve the problem in the setting of Riedel (Econometrica 77(3):857–908, 2009). As in the classical case, it is optimal to stop if the current observation is a running maximum that exceeds certain decreasing thresholds. We characterize the history dependent minimizing measure and perform sensitivity analysis on two examples.

Suggested Citation

  • Lazar Obradović, 2020. "Robust best choice problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 435-460, December.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:3:d:10.1007_s00186-020-00719-5
    DOI: 10.1007/s00186-020-00719-5
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    References listed on IDEAS

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    1. Marek Skarupski, 2019. "Full-information best choice game with hint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 153-168, October.
    2. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
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    6. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    7. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    9. Małgorzata Kuchta, 2017. "Iterated full information secretary problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 277-292, October.
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    Cited by:

    1. Chi Seng Pun, 2022. "Robust classical-impulse stochastic control problems in an infinite horizon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 291-312, October.
    2. Martin Meier & Leopold Sögner, 2023. "Hunting for superstars," Mathematics and Financial Economics, Springer, volume 17, number 1, June.

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