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Optimal bookmaking

Author

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  • Lorig, Matthew
  • Zhou, Zhou
  • Zou, Bin

Abstract

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks an optimal price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or characterizations to the bookmaker’s optimal bookmaking problem in various interesting models.

Suggested Citation

  • Lorig, Matthew & Zhou, Zhou & Zou, Bin, 2021. "Optimal bookmaking," European Journal of Operational Research, Elsevier, vol. 295(2), pages 560-574.
    • Handle: RePEc:eee:ejores:v:295:y:2021:i:2:p:560-574
    DOI: 10.1016/j.ejor.2021.03.005
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    References listed on IDEAS

    as
    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    2. �lvaro Cartea & Sebastian Jaimungal, 2015. "Optimal execution with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1279-1291, August.
    3. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    4. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    5. Peter Divos & Sebastian Del Bano Rollin & Zsolt Bihari & Tomaso Aste, 2018. "Risk-Neutral Pricing and Hedging of In-Play Football Bets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(4), pages 315-335, July.
    6. Klaassen, Franc J. G. M. & Magnus, Jan R., 2003. "Forecasting the winner of a tennis match," European Journal of Operational Research, Elsevier, vol. 148(2), pages 257-267, July.
    7. Song, Kai & Shi, Jian, 2020. "A gamma process based in-play prediction model for National Basketball Association games," European Journal of Operational Research, Elsevier, vol. 283(2), pages 706-713.
    8. Stewart Hodges & Hao Lin & Lan Liu, 2013. "Fixed Odds Bookmaking with Stochastic Betting Demands," European Financial Management, European Financial Management Association, vol. 19(2), pages 399-417, March.
    9. Lode Li, 1988. "A Stochastic Theory of the Firm," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 447-466, August.
    10. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    11. Adrian, Tobias & Capponi, Agostino & Fleming, Michael & Vogt, Erik & Zhang, Hongzhong, 2020. "Intraday market making with overnight inventory costs," Journal of Financial Markets, Elsevier, vol. 50(C).
    12. Bozóki, Sándor & Csató, László & Temesi, József, 2016. "An application of incomplete pairwise comparison matrices for ranking top tennis players," European Journal of Operational Research, Elsevier, vol. 248(1), pages 211-218.
    13. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    14. Lijun Bo & Agostino Capponi, 2016. "Optimal Investment In Credit Derivatives Portfolio Under Contagion Risk," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 785-834, October.
    15. Pashigian, B Peter, 1988. "Demand Uncertainty and Sales: A Study of Fashion and Markdown Pricin g," American Economic Review, American Economic Association, vol. 78(5), pages 936-953, December.
    16. Andrew Grant & Anastasios Oikonomidis & Alistair C. Bruce & Johnnie E. V. Johnson, 2018. "New entry, strategic diversity and efficiency in soccer betting markets: the creation and suppression of arbitrage opportunities," The European Journal of Finance, Taylor & Francis Journals, vol. 24(18), pages 1799-1816, December.
    17. Erhan Bayraktar & Alexander Munk, 2016. "High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering," Papers 1605.03653, arXiv.org, revised Mar 2017.
    18. Sebastian del Bano Rollin & Zsolt Bihari & Tomaso Aste, 2018. "Risk-Neutral Pricing and Hedging of In-Play Football Bets," Papers 1811.03931, arXiv.org.
    19. Thaler, Richard H & Ziemba, William T, 1988. "Parimutuel Betting Markets: Racetracks and Lotteries," Journal of Economic Perspectives, American Economic Association, vol. 2(2), pages 161-174, Spring.
    20. Lijun Bo & Agostino Capponi & Peng‐Chu Chen, 2019. "Credit portfolio selection with decaying contagion intensities," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 137-173, January.
    21. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    22. Müller, Oliver & Simons, Alexander & Weinmann, Markus, 2017. "Beyond crowd judgments: Data-driven estimation of market value in association football," European Journal of Operational Research, Elsevier, vol. 263(2), pages 611-624.
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