Fuzzy Insurance

Fuzzy set theory is a recently developed field of mathematics that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained m a given set, in fuzzy set theory the transition between membership and non-membership is gradual The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or all-defined to be analyzed by conventional methods This paper alms at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a "preferred policyholder" in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums. Keywords: Fuzzy set theory; preferred policyholders in life insurance, optimal XL-retentions; net single premiums for pure endowment insurance