Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework

Lin He and Zongxia Liang

Insurance: Mathematics and Economics, 2013, vol. 53, issue 3, 643-649

Abstract: In this paper, we study the optimal investment strategy in the DC pension plan during the accumulation phase. During the accumulation phase, a pension member contributes a predetermined amount of money as premiums and the management of the pension plan invests the premiums in equities and bonds to increase the value of the accumulation. In practice, most of the DC pension plans have return of premium clauses to protect the rights of the plan members who die during the accumulation phase. In the model, the members withdraw their premiums when they die and the difference between the premium and the accumulation (negative or positive) is distributed among the survival members. From the surviving members’ point of view, when they retire, they want to maximize the fund size and to minimize the volatility of the accumulation. We formalize the problem as a continuous-time mean–variance stochastic optimal control problem. The management of the pension plan chooses the optimal investment strategy, i.e., the proportions invested in equities and bonds, to maximize the mean–variance utility of the pension member at the time of retirement. Using the variational inequalities methods in Björk and Murgoci (2009), we transform the mean–variance stochastic control into Markovian time inconsistent stochastic control, then establish a verification theorem, which is similar to one of He and Liang (2008, 2009) and Zeng and Li (2011), to find the optimal strategy and the efficient frontier of the pension member. The differences of the optimal strategies between the Pension plans with and without the return of premium clauses are studied via the Monte Carlo methods. The impacts of the risk averse level on the optimal strategies is also explored by the numerical methods.

Keywords: DC pension plan; Markovian time inconsistent stochastic control; Mean–Variance stochastic control; Optimal asset allocation; Return of premiums clauses (search for similar items in EconPapers)
JEL-codes: C61 E21 E22 G11 G23 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (21)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668713001352
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:3:p:643-649

DOI: 10.1016/j.insmatheco.2013.09.002

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().