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 soph...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<sub>∞</sub> 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.展开更多
文摘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<sub>∞</sub> 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.
