Abstract

This paper introduces a new way of modelling the diverse beliefs of agents within an economy. We introduce a model in which all agents receive the same stream of information. However, their different beliefs about the system cause them to behave differently, yet still rationally.

In the model there is a single risky asset and the agents differ in their beliefs about the behaviour of this asset. These differences in belief are expressed through a change of measure. The agents seek to maximise their expected utility of consumption under their individual measure. Using this setup, we derive an expression for the state price density of the agents. This enables us to (theoretically) calculate the price of any contingent claim. To illustrate the model further, we then concentrate on the case of log investors. We derive expressions for the stock price and interest rate process. We also fit the model to the Shiller data set, and it appears to behave very reasonably. Furthermore, we exhibit how our model can explain such features as rational overconfidence and the equity premium puzzle.