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Multi-Period Telser’s Safety-First Portfolio Selection Problem in a Defined Contribution Pension Plan

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Abstract

This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser’s safety-first criterion. The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level. By Tchebycheff inequality, Lagrange multiplier technique, the embedding method and Bellman’s principle of optimality, the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function. Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model. Finally, numerical analysis is provided to analyze the effects of the risk control level, the disaster level and the contribution proportion on the disaster probability and the value function. The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.

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Author information

Authors and Affiliations

  1. School of Insurance, Central University of Finance and Economics, Beijing, 102206, China

    Fangbo Li

  2. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, 102206, China

    Huiling Wu

  3. School of Finance, Guangdong University of Foreign Studies, Guangzhou, 510006, China

    Haixiang Yao

Authors
  1. Fangbo Li
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  2. Huiling Wu
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  3. Haixiang Yao
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Corresponding author

Correspondence to Huiling Wu.

Additional information

This research was supported by grants from Innovation Research in Central University of Finance and Economics, National Natural Science Foundation of China under Grant Nos. 11671411, 71871071, 72071051, Guangdong Basic and Applied Basic Research Foundation under Grant No. 2018B030311004, the Key Program of the National Social Science Foundation of China under Grant No. 21AZD071 and the 111 Project under Grant No. B17050.

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Li, F., Wu, H. & Yao, H. Multi-Period Telser’s Safety-First Portfolio Selection Problem in a Defined Contribution Pension Plan. J Syst Sci Complex 36, 1189–1227 (2023). https://doi.org/10.1007/s11424-023-1142-z

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  • DOI: https://doi.org/10.1007/s11424-023-1142-z

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