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Constrained monotone mean--variance investment-reinsurance under the Cram\'er--Lundberg model with random coefficients

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  • Xiaomin Shi
  • Zuo Quan Xu

Abstract

This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business) and invest in a security market consisting of a risk-free asset and multiple risky assets whose excess return rate and volatility rate are allowed to be random. The trading strategy is subject to a general convex cone constraint, encompassing no-shorting constraint as a special case. The optimal investment-reinsurance strategy and optimal value for the MMV problem are deduced by solving certain backward stochastic differential equations with jumps. In the literature, it is known that models with MMV criterion and mean--variance criterion lead to the same optimal strategy and optimal value when the wealth process is continuous. Our result shows that the conclusion remains true even if the wealth process has compensated Poisson jumps and the market coefficients are random.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2405.17841
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    References listed on IDEAS

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    1. Shen, Yang & Zeng, Yan, 2015. "Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 118-137.
    2. 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.
    3. 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.
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    Cited by:

    1. Yuyang Chen & Tianjiao Hua & Peng Luo, 2024. "A robust stochastic control problem with applications to monotone mean-variance problems," Papers 2408.08595, arXiv.org.

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