Risk Analysis in Theory and Practice

So far, we have focused our attention on static, one-period analyses of economic behavior under risk. This has two important limitations. First, it does not capture the dynamic aspects of most decision-making processes. Second, it basically treats uncertainty as a given. In fact, uncertainty is only what decision-makers have not had a chance to learn before they make a decision. This suggests that an important aspect of risk management is information acquisition: The more an agent can learn about his/her economic environment, the less uncertainty he/she faces. We have delayed the analysis of learning for a simple reason. It is a very complex process (e.g., different individuals often process and retain information differently). In this chapter, we develop a multiperiod analysis to investigate the implications of learning for risk management and dynamic decision-making. We focus on individual decisions, leaving the analysis of risk transfers among individuals for the following chapters.
We start with a general model of dynamic decisions for an individual. The individual could be a firm or a household. He/she has a T-period planning horizon. At each period, he/she makes decisions based on the information available at that time. However, under learning, the information can change over time. This requires addressing explicitly the learning process. At the beginning of the planning horizon, the decision-maker has initial wealth w. At period t, he/she makes some decision denoted by x t, t = 1, , T. The individual also faces...