Mathematical Model for the Determination of Optimal Salary in Defined Benefit Pension Plan with Early Retirement, An Application of Smooth-Pasting Condition

Matthew O. Adaji
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Matthew O. Adaji: Department of Mathematics/Statistics, School of Technology, Benue State Polytechnic, Ugbokolo. Nigeria

International Journal of Research and Innovation in Applied Science, 2023, vol. 8, issue 9, 128-144

Abstract: The paper seeks to apply the mathematical model formulated by Adaji, et al (2015) to determine the optimal financial value of the retirement benefit Sf by applying Smooth Pasting condition. We examined the smooth pasting condition (tangency condition) along the optimal point at the boundary for an American put by considering the gradient, ∂V/∂S more closely and found that as long as V(S) coincides with the straight line, K-S gradient equals-1. We used Microsoft excel spread sheet facility to perform the individual computation for the last 25 years of service for University Senior Lecturers and the last 10 years of service for University Professors. The optimal salary Sf was determined by drawing a vertical line from the tangent perpendicularly to the horizontal axis (salary axis). We recommend the applictaion of this model to individuals as well as cooperate organisations so as maximise the expected retirement benefit. Early retirement alternate should be encouraged so that the teeming population of unemployed youths can take up the vacancies created as a result of early retirement.

Date: 2023
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