Prize Lecture to the memory of Alfred Nobel, December 7, 1990.(This abstract was borrowed from another version of this item.)

Prize Lecture to the memory of Alfred Nobel, December 7, 1990.

The following sections are included:BACKGROUNDTHE SEQUENCE OF GAMESALTERNATE SEQUENCE-OF-GAMES FORMALIZATIONSUNENDING GAMESCONCLUSIONSAPPENDIXREFERENCES

ABSTRACT Recently there has been a growing interest in the scenario model of covariance as an alternative to the one‐factor or many‐factor models. We show how the covariance matrix resulting from the scenario model can easily be made diagonal by adding new variables linearly related to the amounts invested; note the meanings of these new variables; note how portfolio variance divides itself into “within scenario” and “between scenario” variances; and extend the results to models in which scenarios and factors both appear where factor distributions and effects may or may not be scenario sensitive.

Abstract : This paper considers optimization problems in which some or all variables must take on integral values. An ability to solve such problems would be valuable in itself and would also allow handling certain kinds of heretofore intractable 'economies of scale'. An automatic algorithm for solving such problems is not given. A general approach susceptible of individual variations, depending upon the problem and the judgment of the user is presented. Two moderate-size examples are presented to illustrate the method. (Author)