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Mean–variance asset–liability management with asset correlation risk and insurance liabilities

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  • Chiu, Mei Choi
  • Wong, Hoi Ying

Abstract

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.

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  • Chiu, Mei Choi & Wong, Hoi Ying, 2014. "Mean–variance asset–liability management with asset correlation risk and insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 300-310.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:300-310
    DOI: 10.1016/j.insmatheco.2014.10.003
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    2. Georgios I. Papayiannis, 2023. "A Framework for Treating Model Uncertainty in the Asset Liability Management Problem," Papers 2310.11987, arXiv.org.
    3. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    5. Li, Danping & Shen, Yang & Zeng, Yan, 2018. "Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 72-86.
    6. Yumo Zhang, 2023. "Robust Optimal Investment Strategies for Mean-Variance Asset-Liability Management Under 4/2 Stochastic Volatility Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-32, March.
    7. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.
    8. Chen, Shumin & Liu, Yanchu & Weng, Chengguo, 2019. "Dynamic risk-sharing game and reinsurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 216-231.

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