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Zimbidis, A. and Haberman, S. (1993) Delay, Feedback & Variability of Pension Contributions & Fund Levels. Insurance Mathematics and Economics, 13, 271-285.
https://doi.org/10.1016/0167-6687(93)90408-H

has been cited by the following article:

• TITLE: Optimal Management of the Pension Contribution Rate Using the H∞-Control Theory

  AUTHORS: Alexandros A. Zimbidis

  KEYWORDS: Defined Benefit Pension Schemes, Pension Contributions and Fund Levels, H∞-Control, Linear Matrix Inequalities

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.12, December 7, 2022

  ABSTRACT: In this paper, we construct a general model for a pension fund when there are time delays in the valuation process. Actually, we use the standard structure of the basic reserve equation in order to rebuild a more sophisticated approach based on the theory of H∞ control. Our model evaluates the incomplete information from the delayed fund valuations—due to the oscillatory pattern for benefit claims and investment experience of the past years—within the context of uncertainty additionally to the randomness which certainly exists. So, we construct estimations for the optimal proposed contribution rates based on a feedback mechanism which is a robust stabilization controller, using typical linear matrix inequalities. Finally, a numerical application is fully investigated to obtain further insight into the problem.