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An Approach to Forming and Managing a Portfolio of Financial Securities by Small and Medium Price-Taking Traders in a Stock Exchange
P. 257–268.
The paper discusses a new approach to developing tools for quantitatively analyzing the financial behavior of small and medium price-taking traders each possessing abilities to predict share price values for a set of financial securities traded in a stock exchange. Tools for forming and managing a trader’s portfolio of securities from this set are proposed. Particularly, it is shown that when the trader can treat share price values from the portfolio as random variables with known (to her) distributions, an optimal portfolio composition is found by solving a linear programming problem. Otherwise, this optimal composition is found as the trader’s equilibrium strategy in an antagonistic two-person game with the stock exchange being the other player. In this game on polyhedra of disjoint player strategies, described by systems of linear equations and inequalities of a balance kind, calculating saddle points is reduced to solving linear programming problems forming a dual pair.
Keywords: portfoliolinear programmingdynamics of financial securitiesprice-taking tradersrandom variable distributionsaddle pointstwo-person games on polyhedral sets of disjoint player strategies
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In book
Issue 359: Modelling, Computation and Optimization in Information Systems and Management Sciences. , Switzerland: Springer, 2015.
Rechmedina S., Haniev A., Suhih V., Вестник Московского университета. Серия 6: Экономика 2025 Т. 60 № 3 С. 40–62
Periods of high market volatility put investors in a situation where conventional decision- making methods are less reliable. To improve returns, market participants need to understand which factors play a big role in portfolio formation. This article analyzes the determinants of Russian stock returns during the Covid-19 and the rise in geopolitical tension in 2022. ...
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Kolesnikov A., Popova S., / Series arXiv "math". 2024.
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely regular topological spaces. We show the connection between the problem of optimal exchange and the optimal ...
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Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
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Gribanov D., Malyshev D., Shumilov I., Operations Research Forum 2024 Vol. 5 Article 32
In our note, we present a very simple and short proof of a new interesting fact about
the faces of an integer hull of a given rational polyhedron. This fact has a complete
analog in linear programming theory and can be useful to establish new constructive
upper bounds on the number of vertices in an integer hull of ...
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Ignatov A., , in: 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. Communications in Computer and Information Science (CCIS, volume 1913)Vol. 1913.: Springer, 2023. P. 173–187.
Modeling protein folding, which is the process by which a protein obtains its spacial shape, still remains a challenging problem. Protein geometry might be simplified by using the coarse-grained models. The highest level of simplification is achieved in HP-models where only polarity of amino acid residues is considered, and the unified monomers are located in nodes ...
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Virtual network services that span multiple data centers are important to support emerging data-intensive applications in fields such as bioinformatics and retail analytics. Successful virtual network service composition and maintenance requires flexible and scalable “constrained shortest path management” both in the management plane for virtual network embedding (VNE) or network function virtualization service chaining (NFV-SC), ...
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Lazarev A. A., Pravdivets N., Nekrasov I., Algorithms 2018 Vol. 11 No. 4 P. 1–13
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Mikheev A. V., В кн.: Современное образование: содержание, технологии, качество. Материалы XXIV международной научно-методической конференции.Т. 2.: СПб.: Издательство СПбГЭТУ "ЛЭТИ", 2018. С. 55–56.
The issue of using the MathCAD software package in a university educational course for learning to solve optimization problems is considered. The advantage of working with this program is shown and its main features are discussed in the appendix to this course. ...
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Khametov V., Shelemekh E. A., Автоматика и телемеханика 2016 № 6 С. 121–144
We establish existence conditions for extremal probability measures, study their
properties, and consider applications of such measures for solving the perfect hedging problem
for American options on incomplete “frictionless” markets with finite horizon. We develop an
algorithm for computing an American option and solve a corresponding new example with this
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Contents of the book is divided into 2 parts of deterministic and stochastic models of Operations Research.
The first part of "Deterministic models of Operations Research" - is the base section, in which the emphasis is on linear programming.
The second part - "Stochastic models of Operations Research" includes a model of reliability and queuing models. This ...
Added: November 13, 2016
Gurvich V., Boros E., Elbassioni K. et al., , in: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015), Leibniz International Proceedings in Informatics (LIPIcs)Vol. 30.: Dagstuhl: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2015. P. 103–115.
We consider finite Markov decision processes (MDPs) with undiscounted total effective payoff. We show that there exist uniformly optimal pure stationary strategies that can be computed by solving a polynomial number of linear programs. We apply this result to two-player zero-sum stochastic games with perfect information and undiscounted total effective payoff, and derive the existence ...
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Belenky A., Applied Mathematics Letters 2007 Vol. 20 No. 7 P. 795–799
The maximin of a function being the minimum function of a sum of two bilinear functions with one and the same first vector argument belonging to a polyhedron is considered on a polyhedron of connected variables forming two second vector arguments of the bilinear functions. It is shown that finding the exact lower estimate of ...
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Belenky A., Egorova L., , in: Optimization and Its Applications in Control and Data Sciences: In Honor of Boris T. Polyak’s 80th Birthday (Springer Optimization and Its Applications)Book 115.: Springer, 2016. P. 51–117.
The paper proposes two new approaches to designing efficient mathematical tools for quantitatively analyzing decision-making processes that small and medium price-taking traders undergo in forming and managing their portfolios of financial instruments traded in a stock exchange. Two mathematical models underlying these approaches are considered. If the trader can treat price changes for each financial ...
Added: October 10, 2016
Matsuk Z., Deari F., Lakshina V. V., Economic Annals-XXI 2016 Vol. 160 No. 7-8 P. 116–120
This paper provides an experimental study on optimal portfolio composition. Data on seven stocks, included in Ukrainian Exchange Index, for the period from January to December 2015 are considered.
The analysis covers descriptive statistics, correlation, and, finally, optimal investment weights, which are calculated using Sharpe ratio. Covariance matrix of returns is estimated by means of generalized ...
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Belenky A., Egorova L., / Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2016. No. 02.
The paper presents two new approaches to modeling the interaction of small and medium price-taking traders with a stock exchange. In the framework of these approaches, the traders can form and manage their portfolios of financial instruments traded on a stock exchange with the use of linear, integer, and mixed programming techniques. Unlike previous authors’ ...
Added: June 27, 2016
Khametov V., Shelemekh E. A., Automation and Remote Control 2015 Vol. 76 No. 9 P. 1616–1634
We establish an existence criterion for the decomposition that generalizes a wellknown uniform Doob decomposition to a set of equivalent probability measures. Based on this criterion, we obtain necessary and sufficient existence conditions for a minimal superhedging (with respect to any measure out of the set of equivalent measures) American option portfolio on an incomplete frictionless market with a ...
Added: March 10, 2016
Khametov V., Shelemekh E. A., Автоматика и телемеханика 2015 № 9 С. 125–149
We establish an existence criterion for the decomposition that generalizes a wellknown uniform Doob decomposition to a set of equivalent probability measures. Based on this criterion, we obtain necessary and sufficient existence conditions for a minimal superhedging (with respect to any measure out of the set of equivalent measures) American option portfolio on an incomplete frictionless market with a ...
Added: March 9, 2016