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5* Stochastic Dominance The search for a measure of risk led us to compare probability distributions with the same mean. In order to compare probability distributions more generally, we set forth the notion of stochastic dominance. Consider a family of stochastic variables indexed by r on the closed interval [0,1]. Let be the distribution function of the stochastic variable . ,r1) if and only if with strict inequality for a set of values of x with positive probability. ,r1) if and only if with strict inequality for a set of values of x with positive probability.
1983. " IMSSS, no. 433. Stanford University. Pratt, J. 1964. " Econometrica 32:122-136. Â < previous page page_38 next page > If you like this book, buy it! < previous page page_39 next page > Page 39 Ross, S. 1981. " Econometrica 49:621-638. , and J. Stiglitz. 1970. " Journal of Economic Theory 2: 315-329. Stiglitz, J. 1969. " Econometrica 37:660-667. Â < previous page page_39 next page > If you like this book, buy it! < previous page page_40 next page > 43 44 Page 40 3 Certainty Equivalence The solution of maximization problems should satisfy two countervailing conditions: it should be as precise as possible, and it should be easy.
Journal of Mathematical Economics 3:121-129. , and J. Stiglitz. 1974. " Journal of Economic Theory 8: 337-360. , and L. Mirman. 1974. " Journal of Economic Theory 8: 361-368. , and L. Mirman. 1981. " Review of Economic Studies 48:271-280. Machina, M. 1983. " IMSSS, no. 433. Stanford University. Pratt, J. 1964. " Econometrica 32:122-136. Â < previous page page_38 next page > If you like this book, buy it! < previous page page_39 next page > Page 39 Ross, S. 1981. " Econometrica 49:621-638. , and J.