Combined functionals as risk measures.
Proceedings of the Bowles Symposium, Atlanta, April 10-11, 2003.
Risk measures are widely used in insurance pricing, portfolio
selection, and in decision-making in general. Two prevalent
classes of risk measures are expected utility (a dollar transform),
and distorted probability (a probability transform). Both approaches
exhibit properties which are not supported by empirical evidence
on decision-making under risk. We propose a combined functional
(dollar and probability transform) which may combine advantages
of both approaches. The present paper develops representation theorems
and axiomatic descriptions, presents applications to decision-making
under risk, premium calculation, and portfolio selection; and includes
numeric and graphical illustrations.
Key words: risk measure, expected utility, distorted probability,
combined functional, premium calculation, portfolio selection,