Working Paper Alfred P. Sloan School of Management Consumption-portfolio Policies: an Inverse Optimal Problem Consumption-portfolio Policies: an Inverse Optimal Problem Consumption-portfolio Policies: an Inverse Optimal Problem"

We study a problem that is the "inverse" of Merton (1971). For a given consumption-portfolio policy, we provide necessary and sufficient conditions for it to be optimal for "some" agent with an increasing, strictly concave, time-additive, and state independent utility function when the risky asset price follows a general diffusion process. These conditions involve a set of consistency and state independency conditions and a partial differential equation satisfied by the consumption-portfolio policy. We also provide an integral formula which recovers the utility function that supports a given optimal policy. The inverse optimal problem studied here should be viewed as a dynamic recoverability problem in financial markets with continuous trading.