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Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach

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  • Wing Fung Chong
  • Gechun Liang

Abstract

This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion (CRRA) forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. We derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive framework for forward investment and consumption under model uncertainty.

Suggested Citation

  • Wing Fung Chong & Gechun Liang, 2024. "Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach," Papers 2410.01378, arXiv.org.
    • Handle: RePEc:arx:papers:2410.01378
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    References listed on IDEAS

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    1. Anis Matoussi & Dylan Possamaï & Chao Zhou, 2015. "Robust Utility Maximization In Nondominated Models With 2bsde: The Uncertain Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 258-287, April.
    2. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    3. Alexander Schied, 2008. "Robust optimal control for a consumption-investment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 1-20, February.
    4. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    5. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.
    6. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    7. 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.
    8. Chong, Wing Fung & Cui, Haoen & Li, Yuxuan, 2023. "Pseudo-model-free hedging for variable annuities via deep reinforcement learning," Annals of Actuarial Science, Cambridge University Press, vol. 17(3), pages 503-546, November.
    9. Lin, Qian & Sun, Xianming & Zhou, Chao, 2020. "Horizon-unbiased investment with ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    10. Nicole El Karoui & Mohamed Mrad, 2013. "An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE," Post-Print hal-00477381, HAL.
    11. Nicole El Karoui & Mohamed Mrad, 2021. "Recover Dynamic Utility from Observable Process: Application to the economic equilibrium," Post-Print hal-01966312, HAL.
    12. 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.
    13. 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.
    14. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Consistent Utility of Investment and Consumption : a forward/backward SPDE viewpoint ," Post-Print hal-01458419, HAL.
    15. Levon Avanesyan & Mykhaylo Shkolnikov & Ronnie Sircar, 2020. "Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem," Finance and Stochastics, Springer, vol. 24(4), pages 981-1011, October.
    16. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    17. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    18. Asimit, Alexandru V. & Boonen, Tim J. & Chi, Yichun & Chong, Wing Fung, 2021. "Risk sharing with multiple indemnity environments," European Journal of Operational Research, Elsevier, vol. 295(2), pages 587-603.
    19. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    20. 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.
    21. Zhou Yang & Gechun Liang & Chao Zhou, 2017. "Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs," Papers 1711.02939, arXiv.org, revised Dec 2018.
    22. Albrecher, Hansjörg & Cani, Arian, 2019. "On randomized reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 67-78.
    23. Juan Li & Wenqiang Li & Gechun Liang, 2020. "A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models," Papers 2005.10660, arXiv.org, revised May 2021.
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