Consumption-Porfolio Policies: An Inverse Optimal Problem (Classic Reprint)

Excerpt from Consumption-Porfolio Policies: An Inverse Optimal Problem

The inverse problem studied here can be viewed as a dynamic recoverability problem in financial markets with continuous trading; see Kurz (1969) and Chang (1988) for related problems. Our objective here is to recover an economic agent's preferences from the observed consumption-portfolio policy that has been specified for a given asset price process. Since our emphasis is in analyzing an individual's consumption-portfolio policy in a continuous time securities market environment, the inverse problem studied here and the solution method employed in this paper are very different from those of Kurz (1969) and Chang who study an inverse problem in the theory of optimal growth.

Cox and Leland (1982) are the first to characterize efficient consumption-portfolio policies when the asset price follows a geometric Brownian motion; also see Black Our contribution in this paper lies in giving a characterization of the efficient consumption-portfolio policies when the asset price follows a general diffusion process. Since our characterization of efficient consumption portfolio policies is derived for a general specification of the price process, we can also use the same approach to answer a related question: Can a given consumption-portfolio policy be optimal for a given utility function and some diffusion price process or for some utility function and some diffusion price process?

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