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)

The general portfolio selection model preliminary results solution to the general portfolio selection model special cases a portfolio selection programme.

Abstract We integrate appealing features of Markowitz’s mean-variance portfolio theory (MVT) and Shefrin and Statman’s behavioral portfolio theory (BPT) into a new mental accounting (MA) framework. Features of the MA framework include an MA structure of portfolios, a definition of risk as the probability of failing to reach the threshold level in each mental account, and attitudes toward risk that vary by account. We demonstrate a mathematical equivalence between MVT, MA, and risk management using value at risk (VaR). The aggregate allocation across MA subportfolios is mean-variance efficient with short selling. Short-selling constraints on mental accounts impose very minor reductions in certainty equivalents, only if binding for the aggregate portfolio, offsetting utility losses from errors in specifying risk-aversion coefficients in MVT applications. These generalizations of MVT and BPT via a unified MA framework result in a fruitful connection between investor consumption goals and portfolio production.

ABSTRACT Levy and Markowitz showed, for various utility functions and empirical returns distributions, that the expected utility maximizer could typically do very well if he acted knowing only the mean and variance of each distribution. Levy and Markowitz considered only situations in which the expected utility maximizer chose among a finite number of alternate probability distributions. The present paper examines the same questions for a case with an infinite number of alternate distributions, namely those available from the standard portfolio constraint set.