Mossin's Theorem Given Random Initial Wealth

Abstract

The purpose of this article is to reexamine Mossin's Theorem under random initial wealth. Conditions necessary and sufficient for Mossin's Theorem depend on the stochastic dependence between risks. The correlation coefficient, however, is not an adequate measure of stochastic dependence in the general expected-utility model, and so other notions of dependence are used to investigate Mossin's Theorem. The inadequacy of the correlation coefficient is illustrated with two counterexamples. Then, using notions of positive and negative dependence measures, we provide necessary and sufficient conditions for a generalized Mossin Theorem to hold. In addition, a generalized Mossin Theorem is interpreted using the notion of a mean preserving spread made popular by Rothschild and Stiglitz (1970). Given a fair premium and dependent stochastic conditions, we show that an individual can obtain a final wealth distribution with less weight in its tails by selecting less than or more than full insurance.