The Portfolio Theorists

Read, Colin

doi:10.1057/9780230362307

Cited by 4 publications

(7 citation statements)

References 31 publications

(35 reference statements)

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“…Let us substitute vector X*, determined by (4), which corresponds to the assigned value of m set , into (17). Then Thus, it is demonstrated that the dispersion of optimum portfolio is the quadratic function of m set .…”

Section: Key Results a Methods For The Formation Of Securities Portfomentioning

confidence: 99%

“…A method for solving this problem and its realization procedure are determined by the nature of uncertainty relative to the real cost of assets, as well as by the level of confidence in adequacy of its accepted analytical descriptions. Traditional approaches to the solution of problem on the formation of securities portfolio employ the technologies of statistical analysis [15] and are based on the theoretical-probabilistic tools [16,17]. However, under conditions of high volatility in the market situation, an analysis of the existing uncertainty is forcedly limited by the small samples of initial data, which leads to unsatisfactory accuracy in the calculation of statistical characteristics of the model.…”

Section: T T Tmentioning

confidence: 99%

“…This approach provides for obtaining very careful, warranting solution, which is not always acceptable. An alternative approach can be based on the description of uncertain parameters of a problem in the terms of theory of fuzzy sets [14][15][16][17][18]. The appropriate mathematical apparatus for solving the optimization problems has been examined insufficiently, which indicates that the problem explored in present work is relevant.…”

Section: Introductionmentioning

confidence: 99%

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Formation of securities portfolio under conditions of uncertainty

Сіра

Katkova

2017

EEJET

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Section: Key Results a Methods For The Formation Of Securities Portfomentioning

confidence: 99%

Section: T T Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Formation of securities portfolio under conditions of uncertainty

Сіра

Katkova

2017

EEJET

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“…However, in conditions of high variability of the market situation, the analysis of the existing uncertainty is forced to be limited to small samples of the initial data, which leads to unsatisfactory accuracy in calculating the statistical characteristics of the model. This circumstance makes it promising to solve the problem of taking into account the emerging real uncertainty using the least demanding mathematical tools to describe this model -the theory of fuzzy sets [14][15][16][17][18][19][20]. The corresponding approach was implemented in [19].…”

Section: Mathematical Sciencesmentioning

confidence: 99%

“…This approach provides an overly cautious, guaranteed solution, which is not always acceptable. An alternative approach can be based on the description of the uncertain parameters of the problem in terms of the theory of fuzzy sets [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Problem of Formation of Securities Portfolio Under Uncertainty Conditions

Раскін

Сіра

Katkova

2019

EUREKA: Physics and Engineering

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The analysis of known methods for solving the problem of forming a portfolio of securities in the face of uncertainty is carried out. Traditionally, the problem is solved under the assumption that for each type of asset, the values of the main statistical characteristics of the random value of their profitability (mathematical expectation and variance) are known. At the same time, the variance of portfolio returns, which is minimized, is used as a criterion for portfolio optimization. Two alternative approaches to solving the formulated problem are proposed. The first of them provides a decision on the criterion of the probability that the random total portfolio return will not be lower than the given. It is assumed that the random return for each type of asset is distributed normally and the statistical characteristics of the respective densities are known. The original problem is reduced to the problem of maximizing the quadratic fractional criterion in the presence of linear constraints. To solve this non-standard optimization problem, a special iterative algorithm is proposed that implements the procedure for sequential improvement of the plan. The method converges and the computational procedure for obtaining a solution can be stopped by any of the standard criteria. The second approach considers the possibility of solving the problem under the assumption that the distribution densities of random asset returns are not known, however, based on the results of preliminary statistical processing of the initial data, estimates of the values of the main numerical characteristics for each of the assets are obtained. To solve the problem, a new mathematical apparatus is used-continuous linear programming, which is a generalization of ordinary linear programming to the case when the task variables are continuous. This method, in the considered problem, is based on solving an auxiliary problem: finding the worst-case distribution density of a random total portfolio return at which this total return does not reach an acceptable threshold with maximum probability. Now the main minimax problem is being solved: the formation of the best portfolio in the worst conditions. The resulting computational scheme leads to the problem of quadratic mathematical programming in the presence of linear constraints. Next, a method is proposed for solving the problem of forming a portfolio of securities, taking into account the real dynamics of the value of assets. The problem that arises in this case is formulated and solved in terms of the general theory of control, using the Riccati equation.

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Kenneth Joseph Arrow. 23 August 1921—21 February 2017

Velupillai¹

2019

Biogr. Mems Fell. R. Soc.

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Kenneth Arrow was a mathematical economist and political scientist who made many ground-breaking contributions to the theory of economics and social values. His great mathematical ability led him to introduce new approaches to theoretical economics and in particular to a series of fundamental theorems in the discipline. These included the Arrow Impossibility Theorem, the two fundamental theorems of welfare economics and the existence of a competitive equilibrium. For these and many other contributions he was awarded the 1972 Nobel Prize in Economics shared with Sir John Hicks. He took a particular interest in computation and computability in economics. He was active and very productive as a researcher for over seven decades and was renowned as a generous and inspiring teacher and colleague.

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The Portfolio Theorists

Cited by 4 publications

References 31 publications

Formation of securities portfolio under conditions of uncertainty

Formation of securities portfolio under conditions of uncertainty

Dynamic Problem of Formation of Securities Portfolio Under Uncertainty Conditions

Kenneth Joseph Arrow. 23 August 1921—21 February 2017

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