Abstract
In this paper, optimal investment strategies for defined contribution (DC) Pension, with extra contribution are studied. Our model permits the plan member to make a defined extra contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset, and in two risky assets. A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution, and extra contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legend transformation, and Dual theory are used to obtain the explicit solution of the optimal investment strategies for constant relative risk aversion (CRRA) utility function. We observed that the plan member will increase the proportion of his wealth to be invested in bond and stock and will reduce the proportion to be invested in cash.
Highlights
A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution, and extra contribution towards the pension fund, is presented
The Hamilton-Jacobi-Bellman (H-J-B) equation, Legend transformation, and Dual theory are used to obtain the explicit solution of the optimal investment strategies for constant relative risk aversion (CRRA) utility function
We observed that the plan member will increase the proportion of his wealth to be invested in bond and stock and will reduce the proportion to be invested in cash
Summary
Recent publications in economic Journals and other reputable Mathematics and Science Journals have brought to light, different methods of optimizing invest-. Some researchers have made various contributions in this direction, in DC Pension Plan. [1] work on, stochastic life styling: optimal dynamic asset allocation for defined contribution pension plans. Various properties and characteristics of the optimal asset allocation strategy, both with and without the presence of non-hedge able salary risk were discussed. The significance of alternative optimal strategy by pension providers was established
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