A Note on Mossin's Theorem for Deductible Insurance Given Random Initial Wealth
18 Pages Posted: 24 Jul 2017 Last revised: 17 Aug 2017
Date Written: October 26, 2016
Mossin's theorem for deductible insurance given random initial wealth is re-examined. For a fair premium, it is shown that a necessary and sufficient condition, in the spirit of the Generalized Mossin Theorem for coinsurance, is impossible using the notion of expectation dependence. Next, it is established that for a fair premium, full insurance will be optimal for a risk-averse individual if the random loss and the random initial wealth are negative quadrant dependent, improving upon an extant result in the literature. In view of a set of examples given in this paper, such a sufficient condition cannot be obtained using the notion of expectation dependence. Finally, for an unfair premium, it is shown that partial insurance will always be optimal, irrespective of the risk preference of the individual as well as the dependence structure between the random loss and the random initial wealth.
Keywords: Deductible insurance; Random initial wealth; Expectation dependence; Quadrant dependence; Regression dependence
JEL Classification: C02, D81, G22
Suggested Citation: Suggested Citation