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Lending decisions with limits on capital available: The polygamous marriage problem

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  • So, Mee Chi
  • Thomas, Lyn C.
  • Huang, Bo

Abstract

In order to stimulate or subdue the economy, banking regulators have sought to impose caps or floors on individual bank's lending to certain types of borrowers. This paper shows that the resultant decision problem for a bank of which potential borrower to accept is a variant of the marriage/secretary problem where one can accept several applicants. The paper solves the decision problem using dynamic programming. We give results on the form of the optimal lending problem and counter examples to further “reasonable” conjectures which do not hold in the general case. By solving numerical examples we show the potential loss of profit and the inconsistency in the lending decision that are caused by introducing floors and caps on lending. The paper also describes some other situations where the same decision occurs.

Suggested Citation

  • So, Mee Chi & Thomas, Lyn C. & Huang, Bo, 2016. "Lending decisions with limits on capital available: The polygamous marriage problem," European Journal of Operational Research, Elsevier, vol. 249(2), pages 407-416.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:2:p:407-416
    DOI: 10.1016/j.ejor.2015.01.047
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    References listed on IDEAS

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    1. Stein, William E. & Seale, Darryl A. & Rapoport, Amnon, 2003. "Analysis of heuristic solutions to the best choice problem," European Journal of Operational Research, Elsevier, vol. 151(1), pages 140-152, November.
    2. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    3. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    4. Chun, Young H., 1999. "Selecting the best choice in the full information group interview problem," European Journal of Operational Research, Elsevier, vol. 119(3), pages 635-651, December.
    5. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    6. Nicole Bäuerle & Jonathan Ott, 2011. "Markov Decision Processes with Average-Value-at-Risk criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 361-379, December.
    7. J. Preater, 1994. "On Multiple Choice Secretary Problems," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 597-602, August.
    8. Richard Van Slyke & Yi Young, 2000. "Finite Horizon Stochastic Knapsacks with Applications to Yield Management," Operations Research, INFORMS, vol. 48(1), pages 155-172, February.
    9. W Zhuang & M Gumus & D Zhang, 2012. "A single-resource revenue management problem with random resource consumptions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(9), pages 1213-1227, September.
    10. Thomas, Lyn C., 2009. "Consumer Credit Models: Pricing, Profit and Portfolios," OUP Catalogue, Oxford University Press, number 9780199232130.
    11. Gregory P. Prastacos, 1983. "Optimal Sequential Investment Decisions Under Conditions of Uncertainty," Management Science, INFORMS, vol. 29(1), pages 118-134, January.
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