The article gives a graphical interpretation of the concept of risk vulnerability. It shows that in a specific context of binary lotteries the assumption of risk vulnerability adds to prudence what the assumption of decreasing absolute risk aversion adds to risk aversion. We end the presentation showing that results can be extended to the concept of multiplicative risk vulnerability.

The existing literature on savings, insurance, and portfolio choices under risk has revealed that quite often comparative statics results depend, among other things, upon the values of the coefficients of relative risk aversion and relative prudence. More specifically the benchmark values for these coefficients are, respectively, one and two. Recently, several papers investigated constraints on the higher degree extensions of the coefficients of relative risk aversion and of relative prudence. The present work provides a unified approach to this question based (...) on the concept of elementary correlation increasing transformations, allowing for a better understanding of changes in risk in the multiplicative case. (shrink)

This paper shows that temperance is the highest order risk preference condition for which spreading N independent and unfair risks provides the highest level of welfare than any other possible allocations of risks. These results are also interpreted through the concept of N-superadditivity of the utility premium. This paper provides a novel application of temperance, not in terms of two risks as it is common, but in terms of N risks.

This note examines the theory of optimal insurance purchasing in the presence of a nonpecuniary background risk. The occurrence of the qualitative uninsurable background loss can increase, decrease or can leave the marginal utility of wealth unchanged, whereas a financial background loss (as in Doherty and Schlesinger, 1883a) always increases it. Existing theorems on the optimal level of insurance and the optimal form of insurance contracts are shown to hold only under restrictive assumptions on the correlation level between risks. The (...) paper shows that sufficient conditions for the validity of the theorems depend not only on the correlation between the insurable and noninsurable losses, but also on the variation of the marginal utility of wealth with respect to the nonpecuniary variable. (shrink)

This paper investigates the link between the total bivariate risk premium and the sum of partial bivariate risk premia. Whereas in the case of small risks, the non interaction between risks is a sufficient condition to obtain the equality between the total risk premium and the sum of partial risk premia, the paper shows that this condition is not sufficient for large risks. The non interaction between risks occurs in two cases: if risks are independent or if individual's marginal utility (...) of one good is independent of the endowment in the other. Without restriction on the utility function, none of these two conditions is sufficient for large risks. If attention is restricted to preferences that exhibit constant absolute risk aversion, the non variability of the marginal utility of good one with respect to variations in endowment in the other remains a sufficient condition, while the independence between risks does not. (shrink)