### Optimal Investment Strategy for a Defined Contributory Pension Plan in Nigeria Using Dynamic Optimization Technique

#### Abstract

**Abstract:**We consider an optimal investment strategy for a defined contributory pension plan in Nigeria using dynamic optimization technique. The Pension Plan Members (PPMs) make contributions continuously into the pension funds. The Pension Fund Administrator (PFA) propose to invest the contributions made by the PPMs into Federal Government of Nigeria (FGN) bond such as construction of roads in Nigeria. They propose that every road constructed must has a tollgate in order to collect toll and make more wealth for the PPMs at time t <= T . We assume that there are Alternative Roads (AR) the drivers may take to their destination without paying toll. The AR may not be good enough for the vehicles to pass smoothly. We assume that Pension Plan Company (PPC) will make more wealth for the PPMs if the Company Roads (CR) are highly motorable. The PPC estimates some percentage of the Gross Returns (GR) at time t to be set aside as the Costs of Roads Construction (CRC). They also estimates some percentage of the Gross-Net Returns (GNR) (i.e. the returns after CRC has been deducted) as Maintenance Costs (MC). They further estimates some percentage of the Gross-Net-Net Returns (GNNR) (i.e. the returns after CRC and MC have been deducted) as Administrative Costs (AC) at time t . Our aim is to find the optimal value of wealth that will accrue to the PPMs over a period of time. We found that the optimal Net Returns (NR) accrued to the PPMs is N6.6434*10

^{14}( N denotes Naira).

**Key words:**Optimal Investment; Defined Contributory; Pension Plan; Dynamic Optimization; Net Returns; Pension Plan Members; Pension Reform Act; Gross-Net-Net Returns; Pension Plan Company

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DOI: http://dx.doi.org/10.3968/j.sms.1923845220120202.004

DOI (PDF): http://dx.doi.org/10.3968/g1582

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