Optimal Investment With Undiversifiable Income Risk

Abstract

This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. the optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton‐Jacobi‐Bellman equation, which is shown to exist and is characterized. the optimal policy is then given from the first‐order conditions of the Hamilton‐Jacobi‐Bellman equation.

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