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Stochastic optimal control of DC pension funds

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  • Gao, Jianwei

Abstract

In this paper, we study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy.

Suggested Citation

  • Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1159-1164
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Han, Nan-Wei & Hung, Mao-Wei, 2015. "The investment management for a downside-protected equity-linked annuity under interest rate risk," Finance Research Letters, Elsevier, vol. 13(C), pages 113-124.
    2. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    3. Han, Nan-wei & Hung, Mao-wei, 2012. "Optimal asset allocation for DC pension plans under inflation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 172-181.
    4. Soriano-Morales, Yazmín Viridiana & Vallejo-Jiménez, Benjamín & Venegas-Martínez, Francisco, 2017. "Impact of the Degree of Relative Risk Aversion, the Interest Rate and the Exchange Rate Depreciation on Economic Welfare in a Small Open Economy," MPRA Paper 76441, University Library of Munich, Germany.
    5. He, Lin & Liang, Zongxia, 2013. "Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 643-649.
    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. 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.
    8. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    9. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    10. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    11. Wu, Huiling & Zhang, Ling & Chen, Hua, 2015. "Nash equilibrium strategies for a defined contribution pension management," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 202-214.
    12. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    13. repec:eee:insuma:v:79:y:2018:i:c:p:210-224 is not listed on IDEAS
    14. Kun Wu & Weixing Wu, 2016. "Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 14(2), pages 167-178, December.
    15. Hassan Dadashi, 2018. "Optimal investment-consumption problem post-retirement with a minimum guarantee," Papers 1803.00611, arXiv.org.
    16. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    17. repec:wsi:afexxx:v:12:y:2017:i:04:n:s2010495217500178 is not listed on IDEAS
    18. repec:bpj:jossai:v:5:y:2017:i:3:p:229-249:n:3 is not listed on IDEAS
    19. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    20. Guan, Guohui & Liang, Zongxia, 2016. "Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 224-237.
    21. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.

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