In this paper, the optimal investment strategy for a defined contribution (DC) pension scheme was modeled with the assumption that the fund is invested partly in riskless assets and partly in risky assets. The market has a constant interest rate, a stochastic volatility that follows the Heston model, the salary is assumed constant over the entire career of the Pension Plan Participant (PPP) and the contribution is a constant proportion of the salary. The CRRA utility function was utilized to obtain a Hamilton-Jacobi-Bellman (HJB) equation. The resulting HJB equation was solved using the Prandtl Asymptotic Matching Method following the works in the literature.

In this paper, we study optimal asset allocation strategy for a defined contribution (DC) pension fund with return of premium clause under Heston's volatility model in mean-variance utility frame work. In this model, members' next of kin are allowed to withdraw their family members' accumulated premium with predetermined interest. Also, investments in one risk free asset and one risky asset are considered to help increase the accumulated funds of the remaining members in order to meet their retirement needs. Using the actuarial symbol, we formulize the problem as a continuous time mean-variance stochastic optimal control problem. We establish an optimization problem from the extended Hamilton Jacobi Bellman equations using the game theoretic approach and solve the optimization problem to obtain the optimal allocation strategy for the two assets, the optimal fund size and also the efficient frontier of the pension members. We analyze numerically the effect of some parameters on the optimal allocation strategy and deduce that as the initial wealth, predetermined interest rate and risk averse level increases, the optimal allocation policy for the risky asset (equity) decreases. Furthermore, we give a theoretical comparison of our result with an existing result and observed that the optimal allocation policy whose return is with predetermined interest is higher compared to that without predetermined interest.

In this study, the effectiveness of Inductive Inquiry and Transmitter of Knowledge models on students’ academic achievement on Circle Geometry and Trigonometry is explored. The main objectives of the study are to expose the groups to Inductive Inquiry and Transmitter of Knowledge models and compare the effectiveness of these modes of teaching in the teaching of circle geometry and trigonometry. The pre-test-post-test experimental design is chosen for this work. It is hypothesized that there would be significant difference between mean achievement scores of these experimental groups on the post-test. The population of the study consisted of all the students of senior secondary two (SS2) class studying in Govt. Sec. School, Bwari, Federal Capital Territory( FCT) Abuja, Nigeria from which a sample of 60 students is drawn using random sampling technique. They were divided into two groups formed through matching on the basis of their pre-test scores; each group consisting of 30 students. One of the groups is randomly chosen as the Inductive Inquiry group and the other as Transmitter of Knowledge group. The independent variable is mode of teaching and the dependent variable is the academic achievement of students. The dependent variable is measured through a 50-item achievement test items generated using the West African Examination Council’s (WAEC) past questions. These questions are used as both pre-test and post-test items. It is found that Inductive Inquiry group performed better than the Transmitter of Knowledge group. This result may be investigated for further confirmation. It is recommended that Inductive Inquiry model be used by teachers of mathematics while teaching the subject to senior secondary classes. A blend of models may be used because there is no single model that is exclusively best for teaching all the topics at all levels to all students, considering individual differences among students.

This study tackled portfolio selection problem for an insurer as well as a reinsurer aiming at maximizing the probability of survival of the Insurer and the Reinsurer, to assess the impact of proportional reinsurance on the survival of insurance companies as well as to determine the condition that would warrant reinsurance according to the optimal reinsurance proportion chosen by the insurer. It was assumed the insurer's and the reinsurer's surplus processes were approximated by Brownian motion with drift and the insurer could purchase proportional reinsurance from the reinsurer and their risk reserves followed Brownian motion with drift. Obtained were Hamilton-Jacobi-Bellman (HJB) equations which solutions gave the optimized values of the insurer's and the reinsurer's optimal investments in the risky asset and the value of the discount rate that would warrant reinsurance as a ratio of their portfolio weights in the risky asset.