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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Esabai, Ase Matthias
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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A MATHEMATICAL APPROACH TO INVESTMENT WITH CHARGE ON BALANCE AND VOLUNTARY CONTRIBUTIONS UNDER WEIBULL MORTALITY FORCE FUNCTION Akpanibah, Edikan Edem; Benneth, Peter; Esabai, Ase Matthias
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp427-440

Abstract

One of the many challenges encountered by most pension fund administrators (PFAs) in the Defined Contribution (DC) pension plan is the determination of a sustainable and suitable investment plan for their members under mortality risk. To achieve this, there is need to develop an optimal portfolio which considers the volatility of the stock market price consisting of one risk-free asset and a risky asset which follows the Heston volatility model (HVM). Also, the portfolio considers additional voluntary contributions (AVC) by members, tax on the stock market price, charge on balance (CB), and the mortality risk of the pension scheme members (PSM) modeled by the Weibull mortality force function. Furthermore, an optimization problem is established from the extended Hamilton Jacobi Bellman (EHJB) equation using variational method. By applying the variable separation technique and mean variance utility, the optimal control strategy (OCS) and the efficient frontier are obtained. Finally, some numerical simulations are presented to study the behavior of the OCS with respect to some sensitive parameters. It was discovered that the composition of the OCS depends on the instantaneous volatility, tax on investment, AVC, risk aversion coefficient (RAC), CB and the correlation coefficient. Hence, the understanding of the behaviour these parameters are very crucial in the determination of OCS.
AN INVESTOR’S OPTIMAL PLAN IN A DC SCHEME WITH REFUND OF CONTRIBUTIONS FOR MORTGAGE HOUSING SCHEME Akpanibah, Edikan Edem; Samaila, Sylvanus Kupongoh; Esabai, Ase Matthias
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1421-1436

Abstract

In this paper, we investigate an investor’s portfolios in a defined contributory (DC) Pension Scheme with return of contributions for a mortgage housing scheme and managerial fees for time-inconsistent utility. A portfolio with a fixed deposit (risk-free asset) and two stocks (risky assets) is taken into consideration, where the stock market prices of the risky assets follow the geometric Brownian motion (GBM) and the instantaneous volatilities form a positive definite matrix. To determine the number of scheme members (SM) interested in the mortgage housing, the Abraham De Moivre function is used. Furthermore, the dynamic programming and game techniques were used to obtain our optimization problem by maximizing the expected utility (mean-variance utility) subject to the SM’s wealth. Using the variable change technique, the optimal value function (OVF), investor’s optimal plan (IOP), and the efficient frontier were obtained under mean variance utility function. . Furthermore, some numerical results of some sensitive parameters such as risk-free interest rate (RIR), risk averse coefficient (RAC), entry age (EA) of SM, managerial charges (MC), optimal fund size (OFS), instantaneous volatilities (IV) and appreciation rates (AR) of the risky assets were presented to explain their impact on the IOP. It was observed that the IOP, which is the fraction of SM’s accumulations invested in the risky assets, is a decreasing function of RIR, RAC, IV, EA, OFS, and MC but an increasing function of the AR.
Co-Authors Akpanibah, Edikan Edem Benneth, Peter Samaila, Sylvanus Kupongoh