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A robust stochastic control problem with applications to monotone mean-variance problems

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  • Yuyang Chen
  • Tianjiao Hua
  • Peng Luo

Abstract

This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with unbounded coefficients. We further show that the robust stochastic control problem shares the same optimal control and optimal value with the stochastic control problem with a mean-variance cost functional. The results obtained are then applied to monotone mean-variance and mean-variance portfolio selection problems and monotone mean-variance and mean-variance investment-reinsurance problems.

Suggested Citation

  • Yuyang Chen & Tianjiao Hua & Peng Luo, 2024. "A robust stochastic control problem with applications to monotone mean-variance problems," Papers 2408.08595, arXiv.org.
    • Handle: RePEc:arx:papers:2408.08595
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    References listed on IDEAS

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    1. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Constrained monotone mean-variance problem with random coefficients," Papers 2212.14188, arXiv.org, revised Aug 2023.
    2. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004. "A geometric approach to multiperiod mean variance optimization of assets and liabilities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1079-1113, March.
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    4. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    5. Xiaomin Shi & Zuo Quan Xu, 2024. "Constrained monotone mean--variance investment-reinsurance under the Cram\'er--Lundberg model with random coefficients," Papers 2405.17841, arXiv.org, revised May 2024.
    6. Jianfeng Liang & Shuzhong Zhang & Duan Li, 2008. "Optioned Portfolio Selection: Models And Analysis," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 569-593, October.
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