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Time-consistent Optimal Portfolio Strategy for Asset-liability Management under Mean-variance Criterion

Author

Listed:
  • Chanjuan Li
  • Zhongfei Li
  • Ke Fu
  • Haiqing Song

Abstract

This paper studies the time-consistent optimal portfolio strategy of an investor with an exogenous liability. Assume that the investor adopts the mean-variance criterion and trades continuously in a market consisting of one risk-free asset and one risky asset; and the price of the risky asset and the value of the exogenous liability are governed by geometric Brownian motions. An extended Hamilton-Jacobi-Bellman equation is derived, and the analytical expressions of the time-consistent optimal portfolio strategy and the mean-variance efficient frontier are obtained. A numerical example is provided to show the results. Our main findings are- (1) introducing an exogenous liability makes the time-consistent optimal portfolio strategy be a stochastic process; (2) the efficient frontier under the time-consistent optimal strategy for asset-liability management is below both the one under the time-consistent optimal strategy in the case of no liability and the one under the pre-commitment optimal strategy for asset-liability management.

Suggested Citation

  • Chanjuan Li & Zhongfei Li & Ke Fu & Haiqing Song, 2013. "Time-consistent Optimal Portfolio Strategy for Asset-liability Management under Mean-variance Criterion," Accounting and Finance Research, Sciedu Press, vol. 2(2), pages 1-89, May.
    • Handle: RePEc:jfr:afr111:v:2:y:2013:i:2:p:89
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    References listed on IDEAS

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    2. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    3. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    4. Xie, Shuxiang, 2009. "Continuous-time mean-variance portfolio selection with liability and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 148-155, August.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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