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Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments

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Abstract

This paper studies a defined contribution (DC) pension fund investment problem with return of premiums clauses in a stochastic interest rate and stochastic volatility environment. In practice, most of pension plans were subject to the return of premiums clauses to protect the rights of pension members who died before retirement. In the mathematical modeling, we assume that a part of pension members could withdraw their premiums if they died before retirement and surviving members could equally share the difference between accumulated contributions and returned premiums. We suppose that the financial market consists of a risk-free asset, a stock, and a zero-coupon bond. The interest rate is driven by a stochastic affine interest rate model and the stock price follows the Heston’s stochastic volatility model with stochastic interest rates. Different fund managers have different risk preferences, and the hyperbolic absolute risk aversion (HARA) utility function is a general one including a power utility, an exponential utility, and a logarithm utility as special cases. We are concerned with an optimal portfolio to maximize the expected utility of terminal wealth by choosing the HARA utility function in the analysis. By using the principle of dynamic programming and Legendre transform-dual theory, we obtain explicit solutions of optimal strategies. Some special cases are also derived in detail. Finally, a numerical simulation is provided to illustrate our results.

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Acknowledgments

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

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tian**, 300387, China

    Hao Chang

  2. Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland, New Zealand

    **ng-jiang Chen

Authors
  1. Hao Chang
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  2. **ng-jiang Chen
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Correspondence to Hao Chang.

Additional information

This paper is supported by the National Social Science Foundation of China (No. 21FJYB042).

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Chang, H., Chen, Xj. Defined Contribution Pension Planning with the Return of Premiums Clauses and HARA Preference in Stochastic Environments. Acta Math. Appl. Sin. Engl. Ser. 39, 396–423 (2023). https://doi.org/10.1007/s10255-023-1050-y

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  • DOI: https://doi.org/10.1007/s10255-023-1050-y

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