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The value of knowing the market price of risk

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  • Katia Colaneri
  • Stefano Herzel
  • Marco Nicolosi

Abstract

This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios: when the market price of risk is observable (the {\em full information case}), and when it is not (the {\em partial information case}). The corresponding market models are complete in the partial information case and incomplete in the other case, hence the two scenarios exhibit rather different features. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximal price that the investor would be willing to pay to get such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time $0$ only (the {\em initial information case}), or during the whole investment period (the {\em dynamic information case}).

Suggested Citation

  • Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2019. "The value of knowing the market price of risk," Papers 1909.07837, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1909.07837
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    Cited by:

    1. Flavio Angelini & Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "Implicit incentives for fund managers with partial information," Computational Management Science, Springer, vol. 18(4), pages 539-561, October.
    2. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Feb 2024.
    3. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org.
    4. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2023. "Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift," Papers 2301.06847, arXiv.org.

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