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The Price of Information

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  • Sebastian Jaimungal
  • Xiaofei Shi

Abstract

When an investor is faced with the option to purchase additional information regarding an asset price, how much should she pay? To address this question, we solve for the indifference price of information in a setting where a trader maximizes her expected utility of terminal wealth over a finite time horizon. If she does not purchase the information, then she solves a partial information stochastic control problem, while, if she does purchase the information, then she pays a cost and receives partial information about the asset's trajectory. We further demonstrate that when the investor can purchase the information at any stopping time prior to the end of the trading horizon, she chooses to do so at a deterministic time.

Suggested Citation

  • Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2402.11864
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    References listed on IDEAS

    as
    1. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    2. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(3), pages 268-294, May.
    3. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    4. Philippe Casgrain & Sebastian Jaimungal, 2019. "Trading algorithms with learning in latent alpha models," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 735-772, July.
    5. Andrew Papanicolaou, 2019. "Backward SDEs for control with partial information," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 208-248, January.
    6. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    7. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    8. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    9. Benes, Václav E. & Karatzas, Ioannis, 1983. "Estimation and control for linear, partially observable systems with non-gaussian initial distribution," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 233-248, March.
    10. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    11. Banerjee, Snehal & Breon-Drish, Bradyn, 2020. "Strategic trading and unobservable information acquisition," Journal of Financial Economics, Elsevier, vol. 138(2), pages 458-482.
    12. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
    13. Detemple, Jerome B, 1986. "Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-391, June.
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