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- Title
Optimal Portfolio and Strategic Consumption Planning in a Life-Cycle of a Pension Plan Member in a Defined Contributory Pension Scheme.
- Authors
Nwozo, C. R.; Nkeki, C. I.
- Abstract
We study the optimal portfolio and strategic life-cycle consumption process in a defined contributory pension plan. The pension plan members (PPMs) contribute flow of cash into the pension funds. These flow of cash are invested into a market structure that is characterized by a risk-free asset (cash account) and a risky asset (stock) by the pension fund administrator (PFA). The risk-free rate is assume to be deterministic. We find an explicit analytical solution to the non-linear partial differential equation (Hamilton Jacobi Bellman equation (HJB)) that arises from our problem. Also, we find that part of the portfolio value is proportional to the ratio of the present value of expected future contributions to the optimal portfolio value at time t. We further observe that the portfolio of the PPM will grow without bound, if the coefficient of the utility function is close to one, provided the expected growth rate of the risky asset is greater than the short term interest rate. We find an interesting result that shows that as the market evolve, part of the portfolio value should be transferred to the cash account overtime in order to offset unforeseen market shocks that may occur in future time. Also, we find that with the use of power utility function, the inflation risks that is associated with the PPM's contributions is hedged.
- Subjects
PENSION trusts; PENSION fund administration services; NUMERICAL solutions to partial differential equations; PRICE inflation; UTILITY functions; INDUSTRIAL organization (Economic theory); CASH flow
- Publication
IAENG International Journal of Applied Mathematics, 2011, Vol 41, Issue 4, p299
- ISSN
1992-9978
- Publication type
Article