Knowledge that Transforms

Stochastic Dominance rules are playing an increasingly prominent role in the literature on choice under uncertainty. Their foundation is the mainstream VonNeumann-Morgenstern expected utility paradigm. Their essence is to provide an admissible set of choices under restrictions on the utility functions that follow from prevalent and appealing modes of economic behavior: The admissible sets generated are useful for a large group of individual decision makers and the optimal choice for an individual can then be obtained from among the smaller set of admissible choices.

Of the behavioral recommendations garnered from modern capital market theory, few, if any, generalizations have been documented as convincingly as the simple advice to hold several assets in one's portfolio. Sharpe made such a conclusion perfectly clear when he stated [27, p. 184]:If the market is efficient and if an investor is privy to no special information or predictive power, what should he do? First, and most important: diversify.

Michael J. Brennan, Eduardo S. Schwartz, Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis, The Journal of Financial and Quantitative Analysis, Vol. 13, No. 3 (Sep., 1978), pp. 461-474