Pension, being regular payments made to retirees or their beneficiaries after retiring from active service, needs efficient and effective management because of the funds involved as the living standard of the retirees and their dependents rest on it after retirement. In attempt to maximize the wealth of pension contributors, the investors may end up losing the pension fund assets because higher returns on investment go hand in hand with higher risk of loss of invested contributions/savings. This can shatter the hope of not just the contributors/investors but also the entire country as a whole. This research has developed and modified the Dynamic Accumulation Model (DAM) and Risk Minimizing Model (RMM) to aid the optimal fund selection among the four (4) types of fund available in Contributory Pension Scheme (CPS) in Nigeria in order to solve the problem of safety or uncertainty of invested amount. The models strike a balance between the objectives of wealth maximization and risk minimization of pension fund investment in Nigeria.