Abstract
An insurance premium principle is a way of assigning to every risk a real number, interpreted as a premium for insuring risk. There are several methods of defining the principle. In this paper, we deal with the principle of equivalent utility under the rank-dependent utility model. The principle, generated by utility function and probability distortion function, is based on the assumption of the symmetry between the decisions of accepting and rejecting risk. It is known that the principle of equivalent utility can be uniquely extended from the family of ternary risks. However, the extension from the family of binary risks need not be unique. Therefore, the following problem arises: characterizing those principles that coincide on the family of all binary risks. We reduce the problem thus to the multiplicative Pexider functional equation on a region. Applying the form of continuous solutions of the equation, we solve the problem completely.
Highlights
Assume that (Ω, F, P) is a nonatomic probability space and that X is a family of all bounded random variables on (Ω, F, P)
The principle of equivalent utility is a method of insurance contract pricing
It is based on the assumption of symmetry between the decisions of accepting and rejecting risk
Summary
Assume that (Ω, F , P) is a nonatomic probability space and that X is a family of all bounded random variables on (Ω, F , P). Elements of X+ represent the risk to be insured by an insurance company. An insurance contract pricing consists of assigning to any X ∈ X+ a nonnegative real number, interpreted as a premium for insuring X. One of the methods of insurance contract pricing is the principle of equivalent utility introduced by Bühlmann [1]. Assume that the insurance company possesses a preference relation over the elements of X+. Such a relation induces the indifference relation ∼ on
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