Optimal Asset Allocation for HARA Consumers with Labour Income

We take into account: (i) a set of stochastic investment opportunities, (ii) a set of risky assets, (iii) a stochastic riskless interest rate, (iv) stochastic labour incomes, and (v) HARA preferences. Without specifying any particular functional form for drifts and diffusions of all the stochastic variables, we show a quasi-explicit solution for optimal consumption and asset allocation. We demonstrate that the agent behaves as if he could rely on his wealth augmented by the expected present value of all his future labour incomes. The solutions for CRRA and log-preferences are obtained as particular cases of our more general setting. We underline that our computations are based on both the martigale equivalent measure and another “subjective” probability measure depending on the preference parameters.