IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p690-d353188.html
   My bibliography  Save this article

An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers

Author

Listed:
  • Georgy Sofronov

    (Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia)

Abstract

An asset selling problem is one of well-known problems in the decision making literature. The problem assumes a stream of bidders who would like to buy one or several identical objects (assets). Offers placed by the bidders once rejected cannot be recalled. The seller is interested in an optimal selling strategy that maximizes the total expected revenue. In this paper, we consider a multi-asset selling problem when the seller wants to sell several identical assets over a finite time horizon with a variable number of offers per time period and no recall of past offers. We consider the problem within the framework of the optimal stopping theory. Using the method of backward induction, we find an optimal sequential procedure which maximizes the total expected revenue in the selling problem with independent observations.

Suggested Citation

  • Georgy Sofronov, 2020. "An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:690-:d:353188
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/690/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/690/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.
    3. Chun, Young H. & Plante, Robert D. & Schneider, Helmut, 2002. "Buying and selling an asset over the finite time horizon: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 136(1), pages 106-120, January.
    4. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2017. "Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 487-518, June.
    5. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey: Part I," Economic Inquiry, Western Economic Association International, vol. 14(2), pages 155-189, June.
    6. David, Israel, 1998. "Explicit results for a class of asset-selling problems," European Journal of Operational Research, Elsevier, vol. 110(3), pages 576-584, November.
    7. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
    8. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    9. J. MacQueen & R. G. Miller, 1960. "Optimal Persistence Policies," Operations Research, INFORMS, vol. 8(3), pages 362-380, June.
    10. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.
    11. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    12. Donald B. Rosenfield & Roy D. Shapiro & David A. Butler, 1983. "Optimal Strategies for Selling an Asset," Management Science, INFORMS, vol. 29(9), pages 1051-1061, September.
    13. Lippman, Steven A & McCall, John J, 1976. "The Economics of Job Search: A Survey," Economic Inquiry, Western Economic Association International, vol. 14(3), pages 347-368, September.
    14. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hugh N. Entwistle & Christopher J. Lustri & Georgy Yu. Sofronov, 2022. "On Asymptotics of Optimal Stopping Times," Mathematics, MDPI, vol. 10(2), pages 1-18, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Georgy Yu. Sofronov, 2020. "An Optimal Double Stopping Rule for a Buying-Selling Problem," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 1-12, March.
    2. Sofronov, Georgy, 2013. "An optimal sequential procedure for a multiple selling problem with independent observations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 332-336.
    3. Rebecca Dizon-Ross & Sheldon M. Ross, 2020. "Dynamic search models with multiple items," Annals of Operations Research, Springer, vol. 288(1), pages 223-245, May.
    4. Georgy Yu. Sofronov, 2016. "A multiple optimal stopping rule for a buying–selling problem with a deterministic trend," Statistical Papers, Springer, vol. 57(4), pages 1107-1119, December.
    5. 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.
    6. Chun, Young Hak, 1997. "Rank-based selection strategies for the random walk process," European Journal of Operational Research, Elsevier, vol. 96(2), pages 417-427, January.
    7. Chun, Young H. & Plante, Robert D. & Schneider, Helmut, 2002. "Buying and selling an asset over the finite time horizon: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 136(1), pages 106-120, January.
    8. Churlzu Lim & J. Neil Bearden & J. Cole Smith, 2006. "Sequential Search with Multiattribute Options," Decision Analysis, INFORMS, vol. 3(1), pages 3-15, March.
    9. Hak Chun, Young, 1996. "Selecting the best choice in the weighted secretary problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 135-147, July.
    10. Ee, Mong-Shan, 2009. "Asset-selling problem with an uncertain deadline, quitting offer, and search skipping option," European Journal of Operational Research, Elsevier, vol. 198(1), pages 215-222, October.
    11. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    12. David, Israel & Levi, Ofer, 2004. "A new algorithm for the multi-item exponentially discounted optimal selection problem," European Journal of Operational Research, Elsevier, vol. 153(3), pages 782-789, March.
    13. Vincent Mak & Darryl A. Seale & Amnon Rapoport & Eyran J. Gisches, 2019. "Voting Rules in Sequential Search by Committees: Theory and Experiments," Management Science, INFORMS, vol. 65(9), pages 4349-4364, September.
    14. Ballot, Gerard, 2002. "Modeling the labor market as an evolving institution: model ARTEMIS," Journal of Economic Behavior & Organization, Elsevier, vol. 49(1), pages 51-77, September.
    15. Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C., 2009. "Experiments on unemployment benefit sanctions and job search behavior," European Economic Review, Elsevier, vol. 53(8), pages 937-951, November.
    16. Brigitte Dormont & Denis Fougère & Ana Prieto, 2001. "L'effet de l'allocation unique dégressive sur la reprise d'emploi," Économie et Statistique, Programme National Persée, vol. 343(1), pages 3-28.
    17. Tan Wang & Tony S. Wirjanto, 2016. "Risk Aversion, Uncertainty, Unemployment Insurance Benefit and Duration of "Wait" Unemployment," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 1-34, May.
    18. Armstrong, Mark & Zhou, Jidong, 2010. "Exploding offers and buy-now discounts," MPRA Paper 22531, University Library of Munich, Germany.
    19. Franz Rothlauf & Daniel Schunk & Jella Pfeiffer, 2005. "Classification of Human Decision Behavior: Finding Modular Decision Rules with Genetic Algorithms," MEA discussion paper series 05079, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    20. Masaru Sasaki & Miki Kohara & Tomohiro Machikita, 2013. "Measuring Search Frictions Using Japanese Microdata," The Japanese Economic Review, Japanese Economic Association, vol. 64(4), pages 431-451, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:690-:d:353188. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.