Optimal portfolio and consumption with stochastic salary and inflation hedging strategy for defined contributory pension scheme

Abstract

This paper consider the optimal portfolio and consumption with stochastic salary and inflation protection strategy for a defined contributory pension scheme. It was assume that a Pension Plan Member (PPM) made a stochastic cash inflows, which are invested into a risk-free asset (cash account), stocks and inflation-linked bonds. Due to high risk of inflation and diminishing value of pension benefits, Pension Fund Administrators (PFAs) starts investing the contributions of the PPM in inflation-linked bonds. The paper presents the value of the PPM's wealth at time $t$. A solution technique was constructed to provide analytical solution to our resulting Hamilton-Jacobi-Bellman (HJB) equation. The optimal consumption and variational form of Merton portfolio demand for stocks, inflation-linked bonds (indexed bonds) and cash account were obtained. The optimal portfolio values for inflation-linked bonds includes an inter-temporal hedging term that offset any shock to the stochastic contribution of the PPM. It was found that the terminal consumption depend on the initial wealth, the present value of future contributions, coefficients of relative risk aversion and the discount (preference) rate which captures the PPM's preference over time.