Introduction

We have thus far limited ourselves to a model of two-date security markets in which securities are traded only once before their payoffs are realized. This model is most suitable for the study of the risk–return relation for securities and the role of securities in the equilibrium allocation of risk.

In the two-date model all uncertainty is resolved at once. It is more realistic to assume that uncertainty is resolved only gradually. As the uncertainty is resolved, agents trade securities again and again. The multidate model of this and the following chapters allows for the gradual resolution of uncertainty and the retrading of securities as new information about security prices and payoffs becomes available.

Uncertainty and Information

In the multidate model, just as in the two-date model, uncertainty is specified by a set of states S. Each of the states is a description of the economic environment for all dates t = 0, 1, …, T. At date 0 agents do not know which state will be realized. But as time passes, they obtain more and more information about the state. Then, at date T, the actual state becomes known to them.

Formally, the information of agents at date t is described by a partition Ft of the set of states S (a partition Ft of S is a collection of subsets of S such that each state s belongs to exactly one element of Ft).