An intertemporal model of consumption and portfolio allocation

We develop an infinite time horizon, continuous time model of portfolio choice and consumption allocation for an investor seeking to maximize the expected utility of his life-time consumption. In this model, the investor is endowed with capital that can be invested in long-lived capital assets and has, in addition, a stochastic stream of cash flows that could be interpreted as either a wage income stream or a stochastic endowment flow. We obtain a complete and original solution to the consumption-portfolio choice problem for the negative exponential and quadratic utility functions and special case solutions for the general power and log utility functions. The results obtained in this paper have significant implications for the theory of asset prices, the theory of mutual funds, optimal portfolio strategies of investors, and so forth. The results of the model can also be easily extended to one with a finite time horizon.