Some Remarks on the Mossin Theorem

Abstract

We establish several new results regarding the Mossin Theorem under both non-random initial wealth and random initial wealth. For the non-random initial wealth case, we show that the Mossin Theorem holds for any constrained class of insurance contracts whose maximum coverage provides full coverage of the potential loss. This result not only settles an open conjecture, but also provides a unified treatment for extant varieties of the Mossin Theorem. For the random initial wealth case, we give a thorough study of the upper-limit insurance. In particular, we show that (i) for a fair premium, the Generalized Mossin Theorem for coinsurance, does not hold for upper-limit insurance, and (ii) for an unfair premium, partial insurance will always be optimal, regardless of the risk preference of the individual and the dependence structure between the random loss and the random initial wealth.

Keywords: Coinsurance; Deductible insurance; Upper-limit insurance; Random initial wealth; Expectation dependence; Quadrant dependence; Regression dependence; Arbitrary distribution