Stochastic optimal control for DC pensionunder the mean-variance model

ZHANG Chu-bing, RONG Xi-min

Systems Engineering - Theory & Practice ›› 2012 ›› Issue (6) : 1314-1323.

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Systems Engineering - Theory & Practice ›› 2012 ›› Issue (6) : 1314-1323. DOI: 10.12011/1000-6788(2012)6-1314
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Stochastic optimal control for DC pensionunder the mean-variance model

  • ZHANG Chu-bing1,2,3, RONG Xi-min1
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Abstract

More and more countries begin to consider changing from the DB type to DC type for pension. This paper researches the optimal investment problem for DC pension with the target of mean-variance and the risky asset derived by the CEV model. By the stochastic control theory, the paper establishes the HJB equation about the optimal investment of DC pension, obtains the optimal investment strategies through the Legendre transform and duality theory, and finally deduces the effective frontier of the optimal investment of DC pension under the mean-variance model.

Key words

defined-contribution pension / mean-variance / constant elasticity of variance model / stochastic control / optimal investment

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ZHANG Chu-bing , RONG Xi-min. Stochastic optimal control for DC pensionunder the mean-variance model. Systems Engineering - Theory & Practice, 2012(6): 1314-1323 https://doi.org/10.12011/1000-6788(2012)6-1314

References

[1] Boulier J F, Huang S, Taillard G. Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund[J]. Insurance: Mathematics and Economics, 2001, 28: 173-189.
[2] Cairns A J G, Blake D, Dowd K. Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans[J]. Journal of Economic Dynamics and Control, 2006, 30: 843-877.
[3] Deelstra G, Grasselli M, Koehl P F. Optimal investment strategies in the presence of a minimum guarantee[J]. Insurance: Mathematics and Economics, 2003, 33: 189-207.
[4] Xiao J, Zhai H, Qin C. The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts[J]. Insurance: Mathematics and Economics, 2007, 40: 302-310.
[5] Gao J. Stochastic optimal control of DC pension funds[J]. Insurance: Mathematics and Economics, 2008, 42: 1159-1164.
[6] Devolder P, Bosch Princep M, Dominguez Fabian I. Stochastic optimal control of annuity contracts[J]. Insurance: Mathematics and Economics, 2003, 33: 227-238.
[7] Battocchio P, Menoncin F. Optimal pension management in a stochastic framework[J]. Insurance: Mathematics and Economics, 2004, 34: 79-95.
[8] Zhou X, Li D. Continuous-time mean-variance portfolio selection: A stochastic LQ framework[J]. Applied Mathematics and Optimization, 2000, 42: 19-33.
[9] Markowitz H. Portfolio selection[J]. Journal of Finance, 1952, 7: 77-91.
[10] Li D, Ng W L. Optimal dynamic portfolio selection: Multiperiod mean-variance formulation[J]. Mathematical Finance, 2000, 10(3): 387-406.
[11] Chiu M, Li D. Asset and liability management under a continuous-time mean-variance optimization framework[J]. Insurance: Mathematics and Economics, 2006, 39: 330-355.
[12] Wang Z, Xia J, Zhang L. Optimal investment for an insurer: The martingale approach[J]. Insurance: Mathematics and Economics, 2007, 40: 322-334.
[13] Fu C, Lari-Lavassani A, Li X. Dynamic mean-variance portfolio selection with borrowing constraint[J]. European Journal of Operational Research, 2010, 200(1): 312-319.
[14] Dennis P, Mayhew S. Risk-neutral skewness: Evidence from stock options[J]. Journal of Financial and Quantitative Analysis, 2002, 37(3): 471-493.
[15] Cox J C. Notes on option pricing I: Constant elasticity of variance diffusions[R]. Working Paper, Stanford University, 1975.
[16] Cox J C, Ross S A. The valuation of options for alternative stochastic processes[J]. Journal of Financial Economics, 1976, 4: 145-166.
[17] Cox J C. The constant elasticity of variance option pricing model[J]. The Journal of Portfolio Management, 1996, 22: 16-17.
[18] Yuen K C, Yang H, Chu K L. Estimation in the constant elasticity of variance model[J]. British Actuarial Journal, 2001(7): 275-292.
[19] Jones C. The dynamics of the stochastic volatility: Evidence from underlying and options markets[J]. Journal of Econometrics, 2003, 116: 181-224.
[20] Widdicks M, Duck P, Andricopoulos A, et al. The Black-Scholes equation revisited: Symptotic expansions and singular perturbations[J]. Mathematical Finance, 2005, 15: 373-391.
[21] Hsu Y L, Lin T I, Lee C F. Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation[J]. Mathematics and Computer in Simulation 2008, 79: 60-71.
[22] Gao J. Optimal portfolios for DC pension plans under a CEV model[J]. Insurance: Mathematics and Economics, 2009, 44: 479-490.
[23] Gao J. Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model[J]. Insurance: Mathematics and Economics, 2009, 45: 9-18.
[24] Gu M, Yang Y, Li S, et al. Constant elasticity of variance model for proportional reinsurance and investment strategies[J]. Insurance: Mathematics and Economics, 2010, 46: 580-587.
[25] Gao J. An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts[J]. Insurance: Mathematics and Economics, 2010, 46: 511-530.
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