Consumption and Uncertainty in Discrete Time

In this chapter we introduce two types of uncertainty: uncertainty about labor income and uncertainty about returns on financial assets. The intertemporal problem is solved using dynamic programming. When labor income is uncertain, we obtain the well-known result that the level of consumption follows a random walk. When asset returns are uncertain, we show that the allocation of savings among different risky assets depends on the utility function and probability distribution of returns. We then introduce the concept of risk aversion and discuss the role of precautionary saving. Finally, we derive a relationship between intertemporal consumption and portfolio choice.