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Optimal Market-Making with Risk Aversion

Author

Listed:
  • Kan Huang

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • David Simchi-Levi

    (Department of Civil and Environmental Engineering, the Engineering Systems Division and the Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Miao Song

    (Department of Industrial and Manufacturing Systems Engineering, University of Hong Kong, Hong Kong)

Abstract

Market-makers have the obligation to trade any given amount of assets at quoted bid or ask prices, and their inventories are exposed to the potential loss when the market price moves in an undesirable direction. One approach to reduce the risk brought by price uncertainty is to adjust the inventory at the price of losing potential spread gain. Using stochastic dynamic programming, we show that a threshold inventory control policy is optimal with respect to an exponential utility criterion and a mean-variance trade-off model. Symmetric and monotone properties of the threshold levels are also established.

Suggested Citation

  • Kan Huang & David Simchi-Levi & Miao Song, 2012. "Optimal Market-Making with Risk Aversion," Operations Research, INFORMS, vol. 60(3), pages 541-565, June.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:3:p:541-565
    DOI: 10.1287/opre.1120.1039
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    References listed on IDEAS

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    Cited by:

    1. Agostino Capponi & Jos'e E. Figueroa-L'opez & Chuyi Yu, 2021. "Market Making with Stochastic Liquidity Demand: Simultaneous Order Arrival and Price Change Forecasts," Papers 2101.03086, arXiv.org.
    2. Wu, Wei-Shao & Liu, Yu-Jane & Lee, Yi-Tsung & Fok, Robert C.W., 2014. "Hedging costs, liquidity, and inventory management: The evidence from option market makers," Journal of Financial Markets, Elsevier, vol. 18(C), pages 25-48.
    3. Sen Lin & Bo Li & Antonio Arreola-Risa & Yiwei Huang, 2023. "Optimizing a single-product production-inventory system under constant absolute risk aversion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 510-537, October.
    4. Chiu, Chun-Hung & Choi, Tsan-Ming & Hao, Gang & Li, Xun, 2015. "Innovative menu of contracts for coordinating a supply chain with multiple mean-variance retailers," European Journal of Operational Research, Elsevier, vol. 246(3), pages 815-826.
    5. Wen, Xiaoqin & Xu, Chen & Hu, Qiying, 2016. "Dynamic capacity management with uncertain demand and dynamic price," International Journal of Production Economics, Elsevier, vol. 175(C), pages 121-131.
    6. Christopher D. Clack & Elias Court & Dmitrijs Zaparanuks, 2020. "Dynamic Coupling and Market Instability," Papers 2005.13621, arXiv.org.

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