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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
Affiliation:
School of Science, Wuhan University of Technology, Wuhan430072, P.R. China E-mail: [email protected]; [email protected]
Fenge Chen
Affiliation:
School of Science, Wuhan University of Technology, Wuhan430072, P.R. China E-mail: [email protected]; [email protected]

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.

Type
Research Article
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: 101118.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): 195209.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: 105124.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): 173189.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): 843877.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): 397419.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: 137150.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. 225228.Google Scholar
9.Christiansen, M.C. & Steffensen, M. (2013). Deterministic mean-variance-optimal consumption and investment. Stochastics 85(4): 620636.CrossRefGoogle Scholar
10.Christiansen, M.C. & Steffensen, M. (2018). Around the life-cycle: deterministic consumption-investment strategies. North American Actuarial Journal 22(3): 491507.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: 4759.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. 375408.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: 5866.Google Scholar
16.Han, N. & Hung, M. (2012). Optimal asset allocation for the DC pension plans under inflation. Insurance: Mathematics and Economics 51: 172181.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): 231244.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): 233247.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: 416428.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: 202214.Google Scholar
22.Yong, J.M. & Zhou, X.Y. (1999). Stochastic controls: Hamiltionian systems and HJB equations. New York: Springer.CrossRefGoogle Scholar