Nonlinear utility models arising from unmodelled small world intercorrelations

Article Abstract:

The expected utility axioms discussed by Savage in his 1972 work 'Foundations of Statistics' only show the rationality of maximizing utility if people only had to make a single decision in their entire lives. This scenario, of course, is extremely improbable, since people are always confronted by individual decision situations called 'small worlds.' Savage's axioms, however, will imply the optimality of expected utility maximization in small worlds provided that the various small worlds' lotteries are probabilistically independent. In such a case, expected utility axioms will show the optimality of maximizing a nonlinear elation/disappointment utility model.

Nonlinear theories, Decision theory

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One-switch utility functions and a measure of risk

Article Abstract:

Research was conducted on the effects of choosing between two financial gambles as the wealth of the decision maker varies. Results show that individuals will switch from one financial gamble to another at a unique critical wealth level. Decreasing risk aversion does not support the findings, but there is a small class of utility functions which do support the findings. Researchers have identified how the findings lead to a measure of risk. The results of the study are applicable to discounting functions as well as cash flows.

Usage, Choice (Psychology), Risk-taking (Psychology), Risk taking, Marginal utility

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An additive group utility for a fund manager

Article Abstract:

The additive utility formula is transplanted to the context of fund management. Three further axioms are added to the additive utility formula. The weighted group utility formula is deduced with the weight of each individual equal to the inverse of the marginal utility of his investment in the fund. The problem of interpersonal comparisons of utility is eliminated because the group weights make the weighted group utility formula invariant to arbitrary utility transformations.

Investments

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