Том 8

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https://ekmair.ukma.edu.ua/handle/123456789/38082

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Browsing Том 8 by Author "Shchestyuk, Nataliya"

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    Portfolio optimization for real data: approaches and chal-lenges
    (2025) Burdym, Anastasiia; Danyliuk, Yevheniia; Shchestyuk, Nataliya
    Portfolio optimization continues to be a dynamic field within finance, integrating new theories and technologies to better meet investor needs. As financial markets evolve, so too will the methodologies used to optimize portfolios, making it an area ripe for ongoing research and innovation. Classical Markowitz approach is based on the mean-variance optimization, which quantifies the tradeoff between risk (variance) and return (expected return). This approach had some limitations. It assumes investors are rational, markets are efficient, and asset returns are normally distributed. As a response to the some limitations of Markowitz theory minimum-VaR approach was appeared. This theory recognizes some assymetry, that investors are more concerned about potential losses than gains and incorporates downside risk measures like Value-at-Risk. Despite advancements of the classical Markowitz theory and minimum VaR approach, challenges remain in accurately estimating parameters, singularity of the covariance matrix and managing risks in volatile markets. In this paper we consider the mean-variance and mean-Var optimal portfolios and take into account the case when the covariance estimated matrix is singular. We use the Moore-Penrose pseudoinverse and Singular Value Decomposition (SVD) to find solutions. We apply these approaches and methodics to real financial data, construct mean-variance and mean-Var optimal portfolios and compare the dynamics of expected returns (mean), volatility and VaR for it. Thanks to the proposed approaches, the investor gets a tool that allows him to make decisions about choosing an approach to building an optimal portfolio, as well as taking into account the singularity of the covariance matrix.
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    Stochastic experiment for some generalizations ofthe secretary problem
    (2025) Melnyk, Dmytro; Zakhariichenko, Yuri; Shchestyuk, Nataliya
    The paper considers some generalizations of the secretary problem, which is a classic problem inoptimal stopping theory. We assume that the manager is somewhat more flexible and changes his goalto hire one of the top two best candidates. Another generalization is the searching the candidate of thetop 𝜖 percent. It means that we agree to choose the candidate who differs from the absolute leader by nomore than a specified amount (𝜖 percent). Starting with classical secretary problem, we discuss in detailoptimal solution for the secretary problem with the two best, following results in various sources. Wereview some approaches to this problem, which give the same optimal solution. After that we presentour results of the stochastic experiments for both generalizations. By simulating numerous iterations ofthe candidate selection process, we estimate the probability of successfully selecting the best candidate.We demonstrate that with increasing 𝜖, the probability (rate) of success increases, and the number ofcandidates that were previously rejected decreases. Moreover, when we generate a list of candidateswith random quality scores we use a random number generator to assign scores from different kind ofdistribution that reflects the quality of candidates.We conclude that stochastic experiment based on Monte Carlo method is a powerful statistical tech-nique that can be employed to analyze the different generalizations od Secretary ProblemMoreover, the Secretary problem is applied not just in human resources for the searching the bestcandidate, but across various fields: in project management, in resource allocation, in computer science.Thanks to the proposed approaches, the manager or other scientist gets a tools, which allows him touse a strategy that maximizes the chance of stopping with the two or more best candidate and take intoaccount the different kind of distribution that reflects the quality of candidates.