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Multiperiod mean-variance efficient portfolios with endogenous liabilities

Author

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  • Markus Leippold
  • Fabio Trojani
  • Paolo Vanini

Abstract

We study the optimal policies and mean-variance frontiers (MVF) of a multiperiod mean-variance optimization of assets and liabilities (AL). This makes the analysis more challenging than for a setting based on purely exogenous liabilities, in which the optimization is only performed on the assets while keeping liabilities fixed. We show that, under general conditions for the joint AL dynamics, the optimal policies and the MVF can be decomposed into an orthogonal set of basis returns using exterior algebra. This formalism, novel to financial applications, allows us to study analytically the structure of optimal policies and MVF representations under endogenous liabilities in a multidimensional and multiperiod setting. Using a numerical example, we illustrate our methodology by analysing the impact of the rebalancing frequency on the MVF and by highlighting the main differences between exogenous and endogenous liabilities.

Suggested Citation

  • Markus Leippold & Fabio Trojani & Paolo Vanini, 2011. "Multiperiod mean-variance efficient portfolios with endogenous liabilities," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1535-1546.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:10:p:1535-1546
    DOI: 10.1080/14697680902950813
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    Cited by:

    1. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    2. Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    3. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    4. Yao, Haixiang & Lai, Yongzeng & Li, Yong, 2013. "Continuous-time mean–variance asset–liability management with endogenous liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 6-17.
    5. Zhou, Zhongbao & Xiao, Helu & Yin, Jialing & Zeng, Ximei & Lin, Ling, 2016. "Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 187-202.
    6. Yao, Haixiang & Li, Zhongfei & Li, Duan, 2016. "Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability," European Journal of Operational Research, Elsevier, vol. 252(3), pages 837-851.
    7. Yao, Haixiang & Zeng, Yan & Chen, Shumin, 2013. "Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon," Economic Modelling, Elsevier, vol. 30(C), pages 492-500.
    8. Haixiang Yao & Xun Li & Zhifeng Hao & Yong Li, 2016. "Dynamic asset–liability management in a Markov market with stochastic cash flows," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1575-1597, October.

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