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DETERMINISTIC INVESTMENT STRATEGY IN A DC PENSION PLAN WITH INFLATION RISK UNDER MEAN-VARIANCE CRITERION

Published online by Cambridge University Press:  12 May 2020

Xingchun Peng Open the ORCID record for Xingchun Peng [Opens in a new window]  and
Fenge Chen
Xingchun Peng
Affiliation:
School of Science, Wuhan University of Technology, Wuhan 430072, P.R. China E-mail: pxch@whut.edu.cn; lixueyuanchen@whut.edu.cn
Fenge Chen
Affiliation:
School of Science, Wuhan University of Technology, Wuhan 430072, P.R. China E-mail: pxch@whut.edu.cn; lixueyuanchen@whut.edu.cn
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Abstract

This paper studies an optimal deterministic investment problem for a DC pension plan member with inflation risk. We describe the price processes of the inflation-indexed bond and the stock by a continuous diffusion process and a jump diffusion process with random parameters, respectively. The contribution rate linked to the income of the DC plan member is assumed to be a non-Markovian adapted process. Under the mean-variance criterion, we use Malliavin calculus to derive a characterization for the optimal deterministic investment strategy. In some special cases, we obtain the explicit expressions for the optimal deterministic strategies.

Keywords

DC pension plandeterministic investmentinflation riskMalliavin calculusrandom parameter processes

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 201 - 216
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

1.Bäuerle, N. & Rieder, U. (2013). Optimal deterministic investment strategies for insurers. Risks 1: 101–118.CrossRefGoogle Scholar
2.Blake, D., Wright, D., & Zhang, Y.M. (2013). Target-driven investing: optimal investment strategies in defined contribution pension plans under loss aversion. Journal of Economic Dynamics and Control 37(1): 195–209.CrossRefGoogle Scholar
3.Blake, D., Wright, D., & Zhang, Y.M. (2014). Age-dependent investing: optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners. Journal of Economic Dynamics and Control 38: 105–124.CrossRefGoogle Scholar
4.Boulier, J.F., Huang, S.J., & Taillard, G. (2001). Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund. Insurance: Mathematics and Economics 28(2): 173–189.Google Scholar
5.Cairns, A.J., Blake, D., & Dowd, K. (2006). Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics and Control 30(5): 843–877.CrossRefGoogle Scholar
6.Chen, A. & Delong, L. (2015). Optimal investment for a defined-contribution pension scheme under a regime switching model. Astin Bulletin 45(2): 397–419.CrossRefGoogle Scholar
7.Chen, Z., Li, Z.F., Zeng, Y., & Sun, J. (2017). Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk. Insurance: Mathematics and Economics 75: 137–150.Google Scholar
8.Christiansen, M.C. (2015). A variational approach for mean-variance-optimal deterministic consumption and investment. In Glau, K., Scherer, M., & Zagst, R. (eds), Innovations in quantitative risk management. New York: Springer, pp. 225–228.Google Scholar
9.Christiansen, M.C. & Steffensen, M. (2013). Deterministic mean-variance-optimal consumption and investment. Stochastics 85(4): 620–636.CrossRefGoogle Scholar
10.Christiansen, M.C. & Steffensen, M. (2018). Around the life-cycle: deterministic consumption-investment strategies. North American Actuarial Journal 22(3): 491–507.CrossRefGoogle Scholar
11.Delong, L. (2013). Backward stochastic differential equations with jumps and their actuarial and financial applications. London: Springer.CrossRefGoogle Scholar
12.Di Nunno, G., Øksendal, B., & Proske, F. (2009). Malliavin calculus for Lévy processes with applications to finance. Berlin: Springer.CrossRefGoogle Scholar
13.Dong, Y.H. & Zheng, H. (2019). Optimal investment of DC pension plan under short-selling constraints and portfolio insurance. Insurance: Mathematics and Economics 85: 47–59.Google Scholar
14.Geering, H.P., Herzog, F., & Dondi, G. (2010). Stochastic optimal control with applications in financial engineering. In Chinchuluun, A., Pardalos, P.M., Enkhbat, R., & Tseveendorj, I. (eds), Optimization and optimal control: theory and applications. Berlin: Springer, pp. 375–408.CrossRefGoogle Scholar
15.Guan, G.H. & Liang, Z.X. (2014). Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insurance: Mathematics and Economics 57: 58–66.Google Scholar
16.Han, N. & Hung, M. (2012). Optimal asset allocation for the DC pension plans under inflation. Insurance: Mathematics and Economics 51: 172–181.Google Scholar
17.Herzog, F., Dondi, G., & Geering, H.P. (2007). Stochastic model predictive control and portfolio optimization. International Journal of Theoretical and Applied Finance 10(2): 231–244.CrossRefGoogle Scholar
18.Konicz, A.K. & Mulvey, J.M. (2015). Optimal savings management for individuals with defined contribution pension plans. European Journal of Operational Research 243(1): 233–247.CrossRefGoogle Scholar
19.Nualart, D. (2006). The Malliavin calculus and related topics. Berlin: Springer.Google Scholar
20.Peng, X.C. & Hu, Y.J. (2013). Optimal proportional reinsurance and investment under partial information. Insurance: Mathematics and Economics 53: 416–428.Google Scholar
21.Wu, H.L., Zhang, L., & Chen, H. (2015). Nash equilibrium strategies for a defined contribution pension management. Insurance: Mathematics and Economics 62: 202–214.Google Scholar
22.Yong, J.M. & Zhou, X.Y. (1999). Stochastic controls: Hamiltionian systems and HJB equations. New York: Springer.CrossRefGoogle Scholar