270 occurs on an even day of the month, your insurance payment is refunded and your that the premium for full coverage is such that you find this insurance orth its cost Under these circumstances, would you purchase probabilistic insurance: Yes. No N=95[20][80] Although Problem 9 may appear contrived, it is worth noting that probabilistic insurance represents many forms of protective action where one pays a certain cost to reduce the probability of an undesirable event-without eliminating it altogether. The installation of a burglar alarm, the replacement of old tires, and the decision to stop smoking can all be viewed as probabilistic insurance The responses to Problem 9 and to several other variants of the same question indicate that probabilistic insurance is generally unattractive. Apparently, reduc ing the probability of a loss from p to p/2 is less valuable than reducing the probability of that loss from p/2 to 0. In contrast to these data, expected utility theory (with a concave u) implies that w one is just willing to pay a premium y to insure against a probability p of losin x, then one should definitely be willing to pay a smaller premium ry to reduce th probability of losing x from p to (l-r)p, 0<r<l Formally, if one is indifferent between(w-x, P; w, 1-p)and(w-y, then one should prefer probabilistic insurance(w-x, (l-r)p; w-y, rp; w-ry, 1-p)over regular insurance(w -y) To prove this proposition, we show that p(w-x)+(1-p)(w)=(w-y) implies (1-r)p(w-x)+pa(w-y)+(1-p)(w-ry)>a(w-y) without loss of generality, we can set u(w-x)=0 and u(w)=l. Hence, u(w y)=1-p, and we wish to show that (1-p)+(1-p)(w-ry)>1-port(w-ry)>1- theory, because probabilistic insurance appears intuitively riskier than regu insurance, which entirely eliminates the element of risk. Evidently, the intuitive otion of risk is not adequately captured by the assumed concavity of the utility function for wealth The aversion for probabilistic insurance is particularly intriguing because all nsurance is, in a sense, probabilistic. The most avid buyer of insurance remain rulnerable to many financial and other risks which his policies do not cover. There ppears to be a significant difference between robabilistic insurance and what may be called contingent insurance, which provides the certainty of coverage for a Reproduced with permission of the copyright owmer. Further reproduction prohibited without permissioReproduced with permission of the copyright owner. Further reproduction prohibited without permission