TABLE OF CONTENTS This chapter extends the asset pricing model of Chapter 4 in order to include heterogeneous beliefs. The simplest such model features two agents with different beliefs, trading over time in a market for two securities, a risk-free security and a risky security, which can be viewed as the market portfolio. As in Chapter 4, the formal analysis focuses on underlying state prices. The state price model is first developed in this Chapter, and then extended to develop the two-securities model in Chapter 10.
Consider a financial market with two investors. Time is discrete, with a set of dates indexed t = 0 through T. At date 0 an aggregate amount ? 0 is available for consumption by the two investors. At each subsequent date, the aggregate amount available will unfold through a binomial process, growing by either u > 1 or d < 1. Therefore, at date 1, the aggregate amount available will be either ? 1 = u ? 0 or ? 1 = d ? 0. Denote the sequence of up and down moves between dates 1 and t by the symbol x t. A sin Chapter 4, x t is a date event pair.
