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Mean–variance asset–liability management under constant elasticity of variance process

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  • Zhang, Miao
  • Chen, Ping

Abstract

This paper investigates a mean–variance asset–liability management (ALM) problem under the constant elasticity of variance (CEV) process. The company can invest in n+1 assets: one risk-free bond and n risky stocks. The uncontrollable liability process is modelled by a geometric Brownian motion. The feasibility is studied and potential optimal portfolio is proven to be admissible. We derive the efficient frontier and efficient feedback portfolio in terms of the solutions of two backward stochastic differential equations (BSDEs), which do not admit analytical solutions in general. The closed form solutions are obtained under some special cases. Applying the Monte Carlo simulation, we provide several numerical examples to demonstrate how the efficient frontier is influenced by the relevant parameters.

Suggested Citation

  • Zhang, Miao & Chen, Ping, 2016. "Mean–variance asset–liability management under constant elasticity of variance process," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 11-18.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:11-18
    DOI: 10.1016/j.insmatheco.2016.05.019
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    1. Georgios I. Papayiannis, 2023. "A Framework for Treating Model Uncertainty in the Asset Liability Management Problem," Papers 2310.11987, arXiv.org.
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    3. Wong, K.C. & Yam, S.C.P. & Zeng, J., 2019. "Mean-risk portfolio management with bankruptcy prohibition," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 153-172.
    4. Christopher Bayliss & Marti Serra & Armando Nieto & Angel A. Juan, 2020. "Combining a Matheuristic with Simulation for Risk Management of Stochastic Assets and Liabilities," Risks, MDPI, vol. 8(4), pages 1-14, December.
    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. Zhang, Miao & Chen, Ping & Yao, Haixiang, 2017. "Mean-variance portfolio selection with only risky assets under regime switching," Economic Modelling, Elsevier, vol. 62(C), pages 35-42.
    8. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.

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