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Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions

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  • Gechun Liang
  • Moris S. Strub
  • Yuwei Wang

Abstract

We study discrete-time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we find that these processes are inherently myopic in the sense that optimal strategies do not make use of future model parameters even if these are known. Finally, we argue that predictable forward preferences are a viable framework to model human-machine interactions occuring in automated trading or robo-advising. For both applications, we determine an optimal interaction schedule of a human agent interacting infrequently with a machine that is in charge of trading.

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  • Gechun Liang & Moris S. Strub & Yuwei Wang, 2021. "Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions," Papers 2110.08900, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2110.08900
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    References listed on IDEAS

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    1. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    2. Chong, Wing Fung, 2019. "Pricing and hedging equity-linked life insurance contracts beyond the classical paradigm: The principle of equivalent forward preferences," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 93-107.
    3. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    4. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    5. Sergey Nadtochiy & Michael Tehranchi, 2017. "Optimal Investment For All Time Horizons And Martin Boundary Of Space-Time Diffusions," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 438-470, April.
    6. Gechun Liang & Thaleia Zariphopoulou, 2015. "Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE," Papers 1511.04863, arXiv.org, revised Nov 2016.
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    Cited by:

    1. Wing Fung Chong & Gechun Liang, 2024. "Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach," Papers 2410.01378, arXiv.org.
    2. Bahman Angoshtari, 2022. "Predictable Forward Performance Processes in Complete Markets," Papers 2206.03608, arXiv.org, revised Sep 2022.
    3. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org.
    4. Keffert, Henk, 2024. "Robo-advising: Optimal investment with mismeasured and unstable risk preferences," European Journal of Operational Research, Elsevier, vol. 315(1), pages 378-392.
    5. Ng, Kenneth Tsz Hin & Chong, Wing Fung, 2024. "Optimal investment in defined contribution pension schemes with forward utility preferences," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 192-211.

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