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W1248823193 abstract "Let u(x) be a utility function, i.e., a function with u ′( x )>0, u ″( x )<0 for all x . If S is a risk to be insured (a random variable), the premium P = P(x) is obtained as the solution of the equation which is the condition that the premium is fair in terms of utility. It is clear that an affine transformation of u generates the same principle of premium calculation. To avoid this ambiguity, one can standardize the utility function in the sense that for an arbitrarily chosen point y. Alternatively, one can consider the risk aversion which is the same for all affine transformations of a utility function. Given the risk aversion r(x) , the standardized utility function can be retrieved from the formula It is easily verified that this expression satisfies (2) and (3). The following lemma states that the greater the risk aversion the greater the premium, a result that does not surprise." @default.
W1248823193 created "2016-06-24" @default.
W1248823193 creator A5011886232 @default.
W1248823193 date "1982-12-01" @default.
W1248823193 modified "2023-10-12" @default.
W1248823193 title "A Remark on the Principle of Zero Utility" @default.
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W1248823193 doi "https://doi.org/10.1017/s0515036100004700" @default.
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