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Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching

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  • ZHIPING CHEN

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi 710049, P. R. China2Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Shaanxi 710049, P. R. China)

  • LIYUAN WANG

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Shaanxi 710049, P. R. China2Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Shaanxi 710049, P. R. China)

  • PING CHEN

    (Department of Economics, The University of Melbourne, VIC 3010, Australia)

  • HAIXIANG YAO

    (School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, P. R. China)

Abstract

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

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  • Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:06:n:s0219024919500298
    DOI: 10.1142/S0219024919500298
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