استفاده از تئوری لحظه هندسی مربوط به مدیریت پرتفولیو بهینه

In this article, we start with the brief description of the essence of geometric moment theory method for optimization of integrals due to Kemperman [1–3]. Then, we solve several new Moment problems with applications to stock market and financial mathematics. That is, we give methods for optimal allocation of funds over stocks and bonds at maximum return. More precisely, we present here the optimal portfolio management under optimal selection of securities so to maximize profit. The above are done within the models of optimal frontier and optimizing concavity.

Tile main problem we solve here is the optimal allocation of funds over stocks and bonds and at the same time, given certain level of expectation, best choice of securities on the purpose to maximize return. The results are very general so that they stand by themselves as "formulas" to treat other similar stochastic situations and structures far away from the stock market and financial mathematics. The answers to the above described problem are given under two models of investing, the optimal frontier and optimizing concavity, as being the most natural. There are given many examples all motivated from financial mathematics and of course fitting and working well there. The method of proof derives from the geometric moment theory of Kemperman, see [1-3], and several new moment results of very general nature are presented here. We start the article with basic geometric moment review and we show the proving tool we use next repeatedly. To the best of our knowledge this paper is totally new in l i t e r a t u r e as a whole and nothing similar or prior to it in any form exists there. We hope it is well received by the community of mathematical-economists and that can be useful there, by giving some definite real answers to existing questions in optimal portfolio theory. The continuation of this work will be one to derive algorithms out of this theoretical work and create computer software of implementation and work with actual numerical data of the stock market.