A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the object...A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain;indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.展开更多
Modern financial theory, commonly known as portfolio theory, provides an analytical framework for the investment decision to be made under uncertainty. It is a well-established proposition in portfolio theory that whe...Modern financial theory, commonly known as portfolio theory, provides an analytical framework for the investment decision to be made under uncertainty. It is a well-established proposition in portfolio theory that whenever there is an imperfect correlation between returns risk is reduced by maintaining only a portion of wealth in any asset, or by selecting a portfolio according to expected returns and correlations between returns. The major improvement of the portfolio approaches over prior received theory is the incorporation of 1) the riskiness of an asset and 2) the addition from investing in any asset. The theme of this paper is to discuss how to propose a new mathematical model like that provided by Markowitz, which helps in choosing a nearly perfect portfolio and an efficient input/output. Besides applying this model to reality, the researcher uses game theory, stochastic and linear programming to provide the model proposed and then uses this model to select a perfect portfolio in the Cairo Stock Exchange. The results are fruitful and the researcher considers this model a new contribution to previous models.展开更多
文摘A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain;indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.
文摘Modern financial theory, commonly known as portfolio theory, provides an analytical framework for the investment decision to be made under uncertainty. It is a well-established proposition in portfolio theory that whenever there is an imperfect correlation between returns risk is reduced by maintaining only a portion of wealth in any asset, or by selecting a portfolio according to expected returns and correlations between returns. The major improvement of the portfolio approaches over prior received theory is the incorporation of 1) the riskiness of an asset and 2) the addition from investing in any asset. The theme of this paper is to discuss how to propose a new mathematical model like that provided by Markowitz, which helps in choosing a nearly perfect portfolio and an efficient input/output. Besides applying this model to reality, the researcher uses game theory, stochastic and linear programming to provide the model proposed and then uses this model to select a perfect portfolio in the Cairo Stock Exchange. The results are fruitful and the researcher considers this model a new contribution to previous models.
