HEDGING IN INCOMPLETE MARKERS WITH HARA UTILITY

In the context of Merton's original problem of optimal consumption and portfolio choice in continuous time, this paper solves an extension i n which the investor is endowed with a stochastic income that cannot b e replicated by trading the available securities. The problem is treat ed by demonstrating, using analytic and, in particular, 'viscosity sol utions' techniques, that the value function of the stochastic control problem is a smooth solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. The optimal policy is shown to exist and given in a f eedback form from the optimality conditions in the HJB equation. At ze ro wealth, a fixed fraction of income is consumed. For 'large' wealth, the original Merton policy is approached. We also give a sufficient c ondition for wealth, under the optimal policy, to remain strictly posi tive.