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Mean-variance target-based optimisation in DC plan with stochastic interest rate

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  • Francesco Menoncin
  • Elena Vigna

Abstract

We solve a mean-variance optimisation problem of a defined contribution pension scheme in the accumulation phase. The financial market consists of: (i) the risk-free asset, (ii) a risky asset following a GBM, and (iii) a bond driven by a stochastic interest rate following the Vasicek [1977] dynamics. We find a closed-form solution for both the optimal investment strategy and the portfolio efficient frontier. We show that the mean-variance approach is equivalent to a “user-friendly” target-based approach optimisation problem which minimises a quadratic loss function. We show that the ruin probability can be kept under control through the choice of the target level. Numerical applications show that the proportions of bond and risky asset decrease when retirement approaches.

Suggested Citation

  • Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:337
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    Cited by:

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    2. Doddy Ismunandar Bahari & Hermanto Siregar & Sahara Sahara & Handewi Purwati Saliem Rachman, 2019. "Impact of Agricultural Sectors and Income Inequality in Rural Toward Role of Public Education in Decreasing Educational Inequality in Indonesia," International Journal of Economics and Financial Issues, Econjournals, vol. 9(1), pages 151-159.
    3. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    4. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.

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    More about this item

    Keywords

    Mean-variance approach; efficient frontier; stochastic interest rate; defined contribution pension scheme; portfolio selection; risk aversion; ruin probability;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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