Stochastic optimal control of DC pension funds
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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- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- Yuming Li, 1993. "Growth-Security Investment Strategy for Long and Short Runs," Management Science, INFORMS, vol. 39(8), pages 915-924, August.
- 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.
- 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.
- 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.
- 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.
- 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.
- Francesco Menoncin & Olivier Scaillet, 2006. "Optimal asset management for pension funds," Managerial Finance, Emerald Group Publishing, vol. 32(4), pages 347-374.
- Francesco Menoncin, . "Risk management for pension funds," Working Papers ubs0403, University of Brescia, Department of Economics.
- 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.
- 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.
- 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.
- 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.
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