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Optimal Stopping under Ambiguity in Continuous Time

Author

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  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We develop a theory of optimal stopping problems under ambiguity in continuous time. Using results from (backward) stochastic calculus, we characterize the value function as the smallest (nonlinear) supermartingale dominating the payoff process. For Markovian models, we derive an adjusted Hamilton-Jacobi-Bellman equation involving a nonlinear drift term that stems from the agent's ambiguity aversion. We show how to use these general results for search problems and American Options.

Suggested Citation

  • Riedel, Frank, 2010. "Optimal Stopping under Ambiguity in Continuous Time," Center for Mathematical Economics Working Papers 429, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:429
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    File URL: https://pub.uni-bielefeld.de/download/1943934/2319758
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    References listed on IDEAS

    as
    1. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
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    4. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
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    7. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    8. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 207-226, April.
    2. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    3. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    4. repec:diw:diwwpp:dp1228 is not listed on IDEAS

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