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With or without replacement? Sampling uncertainty in Shepp's urn scheme

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  • Kristoffer Glover

Abstract

We introduce a variant of Shepp's classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem's continuous-time analog, we provide bounds on the value function and in the case of a balanced urn (with an equal number of each ball type) an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem.

Suggested Citation

  • Kristoffer Glover, 2019. "With or without replacement? Sampling uncertainty in Shepp's urn scheme," Papers 1911.11971, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:1911.11971
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    1. Liu, Jun & Longstaff, Francis A, 2000. "Losing Money on Arbitrages: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," University of California at Los Angeles, Anderson Graduate School of Management qt48k8f97f, Anderson Graduate School of Management, UCLA.
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    3. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
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