Optimal consumption choices for a ‘large’ investor

Abstract

This paper examines the optimal consumption and investment problem for a ‘large’ investor, whose portfolio choices affect the instantaneous expected returns on the traded assets. Alternatively, our analysis can be interpreted in terms of an optimal growth problem with nonlinear technologies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration of our characterization result, explicit solutions are provided for specific examples involving an agent with logarithmic utilities and a generalized two-factor version of the CCAPM is derived. The analogy of the consumption problem examined in this paper to the consumption problem with constraints on the portfolio choices is emphasized.