Optimal pension fund management in a jump–diffusion environment: Theoretical and empirical studies

Abstract

This paper considers a theoretical and an empirical study of an optimal pension fund in an inflation environment in which the consumption–portfolio selection problem of an investor who faces both diffusion and jump risks was analyzed. Since the time horizon of a pension fund management is relatively long, we put into consideration four background risks which include inflation, interest rate, investment and income risks. A pension plan member (PPM) is expected to contribute continuously a time-consistent proportion of his income into the scheme. These contributions are invested into a market that is characterized by multiple risk-free assets (which include riskless bonds and bank deposit accounts), stocks and index bonds. The risky assets (stocks and index bonds), interest rates and income process are assumed to follow a jump–diffusion process. Real wealth for the plan member is considered. The resulting Hamilton–Jacobi–Bellman equation was solved using dynamic programming approach. From which, the optimal consumption and optimal investments with jump risks were obtained. Empirical data were collected from Nigeria Stock Exchange; National Bureau of Statistics, Nigeria; and Bursary Department, University of Benin, Nigeria. The analyses of the data were carried out using SPSS package in order to obtain the needed information for the parameters in our derived models. The resulting models for optimal portfolio and consumption were solved using MatLab and Mathematica software. We found that inflation, interest rate and income risks have significant influence on the investor’s portfolio values in the risky assets. We also found that as the risk averse coefficient increases, consumption increases and vice versa. Furthermore, we found that an increase in income can lead to an increase in the portfolio risks and vice versa.