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American Options, Multi-armed Bandits, and Optimal Consumption Plans : A Unifying View

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  • Bank, Peter
  • Föllmer, Hans

Abstract

In this survey, we show that various stochastic optimization problems arising in option theory, in dynamical allocation problems, and in the microeconomic theory of intertemporal consumption choice can all be reduced to the same problem of representing a given stochastic process in terms of running maxima of another process. We describe recent results of Bank and El Karoui (2002) on the general stochastic representation problem, derive results in closed form for Lévy processes and diffusions, present an algorithm for explicit computations, and discuss some applications.

Suggested Citation

  • Bank, Peter & Föllmer, Hans, 2003. "American Options, Multi-armed Bandits, and Optimal Consumption Plans : A Unifying View," SFB 373 Discussion Papers 2003,46, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200346
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    References listed on IDEAS

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    1. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach," Finance and Stochastics, Springer, vol. 5(3), pages 275-303.
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    Cited by:

    1. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    2. Su, Xia, 2006. "A New Approach to the Irreversible Investment Problem," Bonn Econ Discussion Papers 21/2006, University of Bonn, Bonn Graduate School of Economics (BGSE).
    3. Bank, Peter & Riedel, Frank, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Bonn Econ Discussion Papers 29/2003, University of Bonn, Bonn Graduate School of Economics (BGSE).
    4. Szimayer, Alex & Maller, Ross A., 2007. "Finite approximation schemes for Lévy processes, and their application to optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1422-1447, October.
    5. Klein, Nicolas, 2013. "Strategic learning in teams," Games and Economic Behavior, Elsevier, vol. 82(C), pages 636-657.
    6. David A. Goldberg & Yilun Chen, 2018. "Polynomial time algorithm for optimal stopping with fixed accuracy," Papers 1807.02227, arXiv.org, revised May 2024.
    7. Peter Bank & Helena Kauppila, 2014. "Convex duality for stochastic singular control problems," Papers 1407.7717, arXiv.org.
    8. Nicolas Klein, 2009. "Free-Riding And Delegation In Research Teams," 2009 Meeting Papers 253, Society for Economic Dynamics.

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