12.2 Utility Functions and Probabilities（12.2效用函数和概率）.pdf

220 UNCERTAINTY (Ch. 12) only a small part of the risk. The money backing up the insurance is paid in advance,so there is no default risk to the insured. From the economists point of view, cat bonds are a form of state contingent security, that is, a security that pays off if and only if some particular event occurs. This conceptwas first introduced by Nobel laure- ate Kenneth J. Arrow in a paper published in 1952and was long thought to be of only theoretical interest. But it turned out that all sorts of options and other derivatives could be best understood using contingent securi- ties. Now Wall Street rocket scientists draw on this 50-year-old work when creating exotic new derivatives suchas catastrophe bonds. 12.2 Utility Functions and Probabilities If the consumer ha.srea.sonablepreferencesabout consumption in different circumstances,then we will be ableto usea utility function to describethese preferences,just a.swe havedone in other contexts. However,the fact that we are considering choice under uncertainty does add a special structure to the choiceproblem. In general, how a personvalues consumption in one state a.scompared tb another will depend on the probability that the state in question will actually occur. In other words, the rate at which I am willing to substitute consumption if it Fainsfor consumption if it doesnt should have something to do with how likely I think it is to rain. The preferencesfor consumption in different states of nature will depend on the belIefsof the individual about how likely those states are. For this rea.son,we will write the utility function a.sdepending on the probabilities a.swell a.son the consumption levels. Suppose that we are considering two mutually exclusive states such a.srain and shine, loss or no loss, or whatever. Let Cl and C2representconsumption in states