Lifetime Investment and Consumption Using a Defined-Contribution Pension Scheme

A two factor stochastic model is introduced for the two phases of a defined-contribution pension scheme. During the accumulation phase of the pension, the scheme member invests part of their stochastic income in a portfolio of a risky stock and a bond in order to build up sufficient funds for retirement. It is assumed that the remainder of their salary pre-retirement is consumed, and that an annuity is purchased at retirement. The optimal asset allocation and consumption pre-retirement maximises the total expected utility of lifetime consumption. Analytical results are found for a CARA utility function adjusted for each phase of the pension scheme. The optimal contribution to the pension scheme and the optimal asset allocation are found and compared both qualitatively and quantitatively with the deterministic model. If the scheme member's income and the asset price are perfectly correlated then the reduced HJB equation is linear and analytical expression for the controls are found for a general income model. If the correlation is imperfect then analytical controls are found for two particular stochastic income models. These controls are in closed-form if the retirement income is derived from a perpetuity