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Stochastic optimal control of DC pension funds

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  • Gao, Jianwei
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4S26612-1/2/0676fbe5238e48503958ddf24e2e3b69
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 3 (June)
    Pages: 1159-1164

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1159-1164

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    Web page: http://www.elsevier.com/locate/inca/505554

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    2. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2004. "Optimal design of the guarantee for defined contribution funds," Journal of Economic Dynamics and Control, Elsevier, vol. 28(11), pages 2239-2260, October.
    3. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    4. Yuming Li, 1993. "Growth-Security Investment Strategy for Long and Short Runs," Management Science, INFORMS, vol. 39(8), pages 915-924, August.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
    7. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
    8. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    9. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 2003. "Optimal investment strategies in the presence of a minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 189-207, August.
    10. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2003. "Optimal investment strategies in the presence of a minimum guarantee," ULB Institutional Repository 2013/7598, ULB -- Universite Libre de Bruxelles.
    11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    12. Vigna, Elena & Haberman, Steven, 2001. "Optimal investment strategy for defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 233-262, April.
    13. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
    14. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2004. "Optimal design of the guarantee for defined contribution funds," ULB Institutional Repository 2013/7602, ULB -- Universite Libre de Bruxelles.
    15. Devolder, Pierre & Bosch Princep, Manuela & Dominguez Fabian, Inmaculada, 2003. "Stochastic optimal control of annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 227-238, October.
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    Cited by:
    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2012. "Income drawdown option with minimum guarantee," Carlo Alberto Notebooks 272, Collegio Carlo Alberto.
    7. 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.

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