A note on convex stochastic dominance

In this paper, we extend Fishburn’s convex stochastic dominance theorem to include any distribution function. This paper also considers risk takers as well as risk averters, and discusses third order stochastic dominance. We apply separation and representation theorems to obtain a concise alternative proof of the theorem. Our results are used to extend a theorem of Bawa et.al. on comparison between a convex combinations of several contiuous distributions and a single continuous distribution. Acknowlegement. Our deepest thanks are given to Professor Bit-Shun Tam for his helpful comments. The first author would also like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement.