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Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

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  • Zongxia Liang
  • Ming Ma

Abstract

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.

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  • Zongxia Liang & Ming Ma, 2020. "Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1035-1072, July.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:3:p:1035-1072
    DOI: 10.1111/mafi.12217
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    References listed on IDEAS

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    4. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org.
    5. David Criens & Lars Niemann, 2022. "Robust utility maximization with nonlinear continuous semimartingales," Papers 2206.14015, arXiv.org, revised Aug 2023.
    6. David Criens & Lars Niemann, 2023. "Robust utility maximization with nonlinear continuous semimartingales," Mathematics and Financial Economics, Springer, volume 17, number 5, June.
    7. Karl-Wilhelm Georg Bollweg & Thilo Meyer-Brandis, 2024. "Mean-Field SDEs driven by $G$-Brownian Motion," Papers 2401.09113, arXiv.org.
    8. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    9. Weixuan Xia, 2023. "Set-valued stochastic integrals for convoluted L\'{e}vy processes," Papers 2312.01730, arXiv.org.

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