Robust time-consistent strategies of DC pension plans with the return of premiums clauses under inflation

Abstract.

This article investigates the robust time-consistent investment strategy for a DC pension plan with model uncertainty under the mean-variance optimization objective. For the avoidance of reductions in investment returns due to inflation risk and premature death of members, an inflation-indexed bond is introduced into the financial market and a return of premium clause is incorporated into the model. By establishing extended Hamilton-Jacobi-Bellman (HJB) equations, the explicit solutions of both the robust precommitment strategy and the robust time-consistent strategy are presented by virtue of the robust optimal control theory and the stochastic dynamic programming approach. Furthermore, two degradation cases are derived in detail. Finally, a numerical example demonstrates the analysis of the obtained results.

Keywords:

• Robust time-consistent strategy
• mean-variance criterion
• inflation risk
• return of premiums clauses
• ambiguity aversion

2020 MR Subject Classification:

• 60H30
• 91G10
• 93E20

Acknowledgments

The authors thank the reviewers for comments and suggestions for improving the quality of this article.

Disclosure statement

The authors declare that we have no relevant financial or non financial competing interests.

Additional information

Funding

This research is supported by the National Social Science Fund of China (No. 21FJYB042) and the Natural Science Foundation of China (No. 72171169).