Single-Agent Consumption and Investment

Abstract

This chapter solves the problem of an agent who begins with an initial endowment and who can consume while also investing in a standard, complete market as set forth in Chapter 1. The objective of this agent is to maximize the expected utility of consumption over the planning horizon, or to maximize the expected utility of wealth at the end of the planning horizon, or to maximize some combination of these two quantities. Except for the completeness assumption, the market model is quite general, allowing the coefficient processes to be stochastic processes that are not even assumed to be Markovian. Specializations of this model to the case of deterministic and even constant coefficients are provided in Sections 3.8 and 3.9. The problem of this chapter is revisited in the context of incomplete markets in Chapter 6.