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- Title
Robust time-consistent strategy for the defined contribution pension plan with a minimum guarantee under ambiguity.
- Authors
Hao, Zhehong; Chang, Hao
- Abstract
This paper investigates the robust time-consistent investment strategy for the defined contribution pension plan with a minimum guarantee in a stochastic interest rate and stochastic inflation environment under the mean-variance criterion. To protect the purchasing power of pension members after retirement, the amount of the minimum guarantee is assumed to be adjusted with the stochastic interest rate and inflation level in the model. The fund manager is considered as ambiguity averse, and her objective is to prevent herself from the worst-case scenario and ensure that the fund wealth exceeds the minimum guarantee at retirement. The ambiguity-averse manager is allowed to invest in a financial market consisting of four assets: a risk-free asset, a nominal zero-coupon bond, an inflation-indexed bond and a stock. The nominal zero-coupon bond and the inflation-indexed bond are designed to hedge against interest rate risk and inflation risk. Following the robust optimal control theory, both the robust time-consistent strategy and the equilibrium value function are derived by an introduction of an auxiliary problem. Some degenerate cases are also provided. Finally, a numerical simulation demonstrates the results obtained.
- Subjects
DEFINED contribution pension plans; INTEREST rates; INFLATION-indexed bonds; OPTIMAL control theory; AMBIGUITY; INTEREST rate risk; CONTROL theory (Engineering)
- Publication
Computational & Applied Mathematics, 2023, Vol 42, Issue 8, p1
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-023-02482-9