Optimal Illusions and the Simplification of Beliefs

Abstract

Following Brunnermeier and Parker (2005), we examine a decision problem in which the agent can manipulate her beliefs to rationalize her behavior and to extract more benefit from her anticipatory feelings. The optimal beliefs are a best compromise between this benefit and the cost of the risk-taking inefficiency that these optimistic beliefs will generate. We show that the optimal beliefs will be degenerated, with a number of states with a positive probability that does not exceed one plus the number of degrees of freedom in the decision problem. For example, in the portfolio problem with "n" independent assets, the optimal beliefs will have no more than "n" states of nature with a positive subjective probability. In the one-safe-one-risky-asset model, we also show that the two possible excess returns with a positive subjective probability are concentrated at the two boundaries of the support of the objective probability distribution. Therefore, we claim that the transformation of probabilities described in Cumulative Prospect Theory, rather than being a genetic characteristic of human beings, corresponds to a natural tendency of rational agents to select beliefs that maximize their intertemporal welfare.

Keywords

Reference

Christian Gollier, Optimal Illusions and the Simplification of Beliefs, June 2011.