This study investigates advanced portfolio optimization techniques that integrate copula functions and GARCH models to enhance risk-adjusted performance in the European stock market. Traditional methods, such as mean-variance optimization, often fail to capture non-linear dependencies and heavy-tailed behaviors observed in financial returns. The copula-GARCH framework addresses these limitations by jointly modeling dependence structures and time-varying volatility. Using high-performance computing (HPC) resources, approximately 10,000 portfolios were simulated to evaluate the effectiveness of different copula-GARCH configurations. Several GARCH-type specifications - standard GARCH, GJR-GARCH, and exponential GARCH (eGARCH) - were tested in combination with various copula families. The analysis focused on EURO STOXX 50 constituents, with model estimation based on 2014-2021 data and out-of-sample backtesting conducted across three market regimes: the bearish year 2022, the bullish recovery in 2023, and the neutral conditions of 2024. Performance was benchmarked against traditional mean-variance and historical Conditional Value at Risk (CVaR) optimization methods. The combination of a Student’s t copula [33, 34] with marginal Student’s t distributions and an eGARCH model consistently outperformed alternatives, achieving lower CVaR values while maintaining favorable return profiles. This configuration demonstrated superior ability to capture tail dependence and asymmetric volatility, which contributed to its robustness across diverse market conditions. The findings confirm that copula-GARCH models provide a more realistic and adaptable framework for portfolio construction under changing market dynamics. By capturing both non-linear dependencies and time-varying volatility, this approach improves downside-risk control without compromising returns. These results highlight the practical value of copula-GARCH optimization for risk-averse investors operating in the European equity market.

As digitalization and artificial intelligence advance, cybersecurity threats intensify, making malware—a type of software installed without authorization to harm users—an increasingly urgent concern. Due to malware's social and economic impacts, accurately modeling its spread has become essential. While diverse models exist for malware propagation, their selection tends to be intuitive, often overlooking the unique aspects of digital environments. Key model choices include deterministic vs. stochastic, planar vs. spatial, analytical vs. simulation-based, and compartment-based vs. individual state-tracking models. In this context, our study assesses fundamental infection spread models to determine those most applicable to malware propagation. It is organized in two parts: the first examines principles of deterministic and stochastic infection models, and the second provides a comparative analysis to evaluate model suitability. Key criteria include scalability, robustness, complexity, workload, transparency, and manageability. Using consistent initial conditions, control examples are analyzed through Python-based numerical methods and agent-based simulations in NetLogo. The findings yield practical insights and recommendations, offering valuable guidance for researchers and cybersecurity professionals in applying epidemiological models to malware spread.

This study analyses factors influencing the likelihood of a student successfully obtaining a degree in Financial Engineering bachelor's program at Riga Technical University (RTU). Statistical and econometric methods, including correlation analysis and logistic regression, are employed to estimate the significance of various factors such as first-year academic results, financial situation, secondary school performance, participation in extracurricular activities while studying at university, and geographical origin. Using data from 2009 to 2024, we identify the main determinants behind the likelihood of graduating from Financial Engineering. One of the significant findings is that students from outside the capital show a significantly higher completion rate than those from Riga, which points to the importance of such factors as motivation, adaptability, and financial constraints. Factors decreasing graduation likelihood include insufficient prior mathematical proficiency, poor performance during the first study year, and financial difficulties, which often lead to dropouts. Conversely, strong academic performance in the first year increases the probability of completing the program. Gender and student mobility programs are also evaluated for their potential impact. The results imply that increasing targeted financial help and offering more comprehensive academic support could improve graduation rates. The findings may be helpful for university administrators to reinforce student support mechanisms, particularly for at-risk groups. Performing the conducted analysis with data on other study programs can further contribute to understanding the factors that might help achieve higher academic success among university students and help RTU refine its educational strategies.

This paper explores advanced portfolio optimization strategies using copula and GARCH models to enhance risk management and profitability in the European stock market. By utilizing high-performance computing (HPC) to conduct extensive simulations on approximately 10,000 portfolios, the study compares the effectiveness of various copula-GARCH models against traditional approaches, such as the mean-variance model. The most effective configuration-identified as a Student’s copula with marginal Student’s distribution and an eGARCH model-was employed to simulate returns and construct optimal portfolios that minimize Conditional Value at Risk (CVaR). The scalability and robustness of this approach offer valuable insights into its practical applications for portfolio management.

As the processes of societal digitalization and the application of artificial intelligence accelerate, the intensity of cybersecurity threats increases accordingly. The purposes behind malware distribution are becoming more criminalized and business oriented. As society becomes increasingly dependent on social networks and digital technologies, and financial, infrastructure, and governance institutions rely more on these technologies, the spread of malware is becoming ever more dangerous. Therefore, it is crucial to predict infection spread risks in a timely manner. Various epidemiological models are used for modeling malware spread, but the choice of specific models is often more intuitive than evidence based. The aim of this article is to assess the suitability of two models from the epidemiological models set, specifically the classic SIR and SIR w/diffusion models, for modeling malware spread. The findings of this study will be valuable for both researchers studying infection spread and cybersecurity specialists.

Analysing real-life data of commodity price dynamics is challenging, there can be non-stationary, non-linear, contain structural breaks. In this paper, we explore whether threshold models are preferable to linear autoregressive models (ARIMA) and whether the logistic smooth transition (LSTAR) model is preferable to the self-exciting threshold autoregressive (SETAR) model for important Latvian food commodity prices. Using historical prices of 16 most popular food products in Latvia over the last 18 years, we assess the goodness of fit of ARIMA (SARIMA), SETAR and LSTAR for each of the most popular commodity prices in Latvia and then compare the out-of-sample forecasts using measures RMSE and MAPE. Although different types of models appear to be most suitable for different commodities, even despite their similarity like fresh pork, chicken and beef, the overarching conclusion is that regime-switching models fit the prices of the majority of products better. ARIMA is the preferred model for some goods for construction of out-of-sample forecasts marginally more often than for the goodness of fit. Nevertheless, threshold models still appear superior in most cases. Additionally, we obtain rather large smoothness coefficients for most LSTAR models, which means that there are no significant reasons to prefer LSTAR to SETAR.

This paper deals with a logistic system consisting of a wholesale store, a retail store and automobiles that are taking part in goods delivery from a wholesale store to a retail store. Assuming random and coming at random time moments demands, we construct a stochastic model for this transport logistic scheme and derive Gaussian approximation for transport and stock level of goods dynamics.

Normal inverse Gaussian (NIG) distribution is a quit a new distribution introduced in 1997. This is distribution, which describes evolution of NIG process. It appears that in many cases NIG distribution describes log-returns of stock prices with a high accuracy. Unlike normal distribution, it has higher kurtosis, which is necessary to fit many historical returns. This gives the opportunity to construct precise algorithms for hedging risks of options. The aim of this work is to evaluate how good NIG distribution can reproduce stock price dynamics and to illuminate future fields of applications.

Normal inverse Gaussian (NIG) distribution is quite a new distribution introduced in 1997. This is distribution, which describes evolution of NIG process. It appears that in many cases NIG distribution describes log-returns of stock prices with a high accuracy. Unlike normal distribution, it has higher kurtosis, which is necessary to fit many historical returns. This gives the opportunity to construct precise algorithms for hedging risks of options. The aim of the present research is to evaluate how well NIG distribution can reproduce stock price dynamics and to illuminate future fields of application.

Abstract This paper deals with stability analysis of pin-jointed beams that are affected to random pulsating load. The stability conditions of a pin-jointed beam are analysed using a mathematical model of the beam characterised by longitudinal force with Poisson characteristics and applying the stochastic modification of the second Lyapunov method.

This paper deals with stability analysis of elastic pipeline containing water flow, the velocity of which is perturbed harmonically under an action of pulsate fluid flow. The stability conditions of the pipeline section are analyzed under assumption of the mathematical model of fluid caused by longitudinal force with Poisson characteristics and application of the stochastic modification of the second Lyapunov method.

Our research studies the construction and estimation of copula-based semi parametric Markov model for the processes, which involved in water flows in the hydro plants. As a rule analyzing the dependence structure of stationary time series regressive models defined by invariant marginal distributions and copula functions that capture the temporal dependence of the processes is considered. This permits to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tails) of a time series. Dealing with utility company data we have found the best copula describing data - Gumbel copula. As a result constructed algorithm was used for an imitation of low probability events (in a hydro power industry) and predictions.

Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG) probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.

Abstract This paper explores an alternative volatility estimation approach discovering the helical structure of Fourier coefficients of volatility wave. Volatility wave is calculated by using wavelet decomposition with consequent logarithmic variance indicator estimation for each decomposed part of the signal and subsequent volatility matrix transform in a specified way. Further, using discrete Fourier transform the Fourier image of obtained volatility wave is analyzed. The Fourier image coefficients of the transformed volatility indicator have a clear helical (spiral) structure that evolves in time. This brings a new understanding of volatility and its evolution process from signal theory (and wavelet theory) perspective. We have found some regularity in the volatility evolution process. The minimum total distance indicator between Fourier coefficients is proposed as a measure of such regularity. This indicator has a nature of volatility lower bound. . Šajā rakstā tiek aplūkoti alternatīvie volatilitātes rādītāji, kas balstīti uz volatilitātes viļņa Furje attēla spirālveida regularitātes mērījumiem. Volatilitātes vilnis tiek iegūts ar veivlet filtrāciju (ar tiešo un apgriezto nepārtraukto viļņu pārveidojumiem), veicot analizējamā signāla (finanšu laikrindu) dekompozīciju ar turpmāko volatilitātes (jeb logaritmiskās dispersijas) pētījumu katrā signālu komponentē. Turpmāk volatilitātes rādītājs tiek pārveidots noteiktā veidā, tā kā ir aprakstīts šai rakstā. Šī pārveidojuma jēdziens ir volatilitātes indikatora mērogošana un lokālo maksimumu izšķiršana. Modificēts volatilitātes rādītājs tiek analizēts mērogošanas rādītāja griezumā katrā laika momentā „tau”. Modificēts volatilitātes rādītājs mērogošanas parametra griezumā veido viļņveida formu, dēvētu par volatilitātes vilni. Ar Furjē analīzi volatilitātes vilnis tiek pārveidots Furjē attēlā. Rezultātā reālās un imaginārās Furjē attēla daļas veido regulārās formas spirālveida struktūru. Furjē attēla regularitāte tiek noteikta ar L1 un L2 rādītājiem, kas tiek aprēķināti, kā minimālā distance starp visiem volatilitātes viļņa Furjē attēla koeficientiem. L1 un L2 rādītāji pēc savas dabas ir alternatīvi volatilitātes rādītāji. Šis raksts atklāj jaunu skatu uz volatilitāti un to evolūciju Furjē attēla koeficientu spirālveida struktūras griezumā. Šī pieeja ļauj prognozēt jaunas finanšu krīzes rašanos В данной статье рассматриваются альтернативные оценки волатильности, основанные на оценке регулярности спиралевидной структуры Фурье образа волн волатильности. Волна волатильности, получаемая с помощью вейвлет-декомпозиции (Прямого Непрерывного вейвлет-преобразования и Обратного Непрерывного вейвлет-преобразования), посредством декомпозиции анализируемого сигнала (финансового временного ряда) с последующим вычислением показателя волатильности (логарифмической дисперсии) для каждого компонента сигнала. Далее показатель волатильности преобразуется согласно преобразованию, описанному в настоящей работе. Суть данного преобразования заключается в масштабировании и выделении линий локальных максимумов для показателя волатильности. В результате преобразования получаем модифицированный показатель волатильности. Модифицированный показатель волатильности анализируется в разрезе показателя масштаба для каждого временного показателя «тау». Модифицированный показатель волатильности в разрезе показателя масштаба образует волнообразную форму, названную волной волатильности. Посредством Фурье анализа волны волатильности выявляется Фурье образ волны волатильности. В результате мнимые и действительные части коэффициентов Фурье образуют четкую спиралевидную структуру регулярной формы. Регулярность или структурность Фурье образа определяется с помощью показателей L1, L2, рассчитываемых как минимальное расстояние между всеми коэффициентами Фурье образа волны волатильности. Показатели регулярности L1, L2 являются альтернативными показателями волатильности. Данная статья открывает новое видение волатильности и её эволюции с точки зрения спиралевидной структуры коэффициентов Фурье образа волны волатильности. Данное видение позволяет открыть новые способы предсказания финансовых кризисов.

This paper explores an alternative volatility estimation approach discovering the helical structure of Fourier coefficients of volatility wave. Volatility wave is calculated by using wavelet decomposition with consequent logarithmic variance indicator estimation for each decomposed part of the signal and subsequent volatility matrix transform in a specified way. Further, using discrete Fourier transform the Fourier image of obtained volatility wave is analyzed. The Fourier image coefficients of the transformed volatility indicator have a clear helical (spiral) structure that evolves in time. This brings a new understanding of volatility and its evolution process from signal theory (and wavelet theory) perspective. We have found some regularity in the volatility evolution process. The minimum total distance indicator between Fourier coefficients is proposed as a measure of such regularity. This indicator has a nature of volatility lower bound.

The paper presents algorithms for insurance technical provisions taking into account losses, which are incurred but not reported. Evaluation of insurance technical provisions for the kinds of insurance, such as Motor Third Party Liability (MTPL) Insurance, Property Insurance and some others, have difficulties in assessing the impact of the losses from insurance claims incurred requiring a longer time for the settlement of insurance claims. These insurance requirements are mainly associated with health insurance in the MTPL Insurance, losses related to compensation for moral injuries, as well as on life care and life-long pension. To run these payments, you need to know the financial indicators for the period of settlement of loss (such as the effective interest rate, investment income, etc.) In the article the procedures for the most accurate forecast possible losses for the expected excess of loss amount for a treaty year are provided, using the loss experience of the previous years of the occurrence with their development. However, certain adjustments should be made to take account of the impact of losses from previous years for the current period. This article describes how outstanding losses have to be projected on a year of reporting, so that they are correspond to the current values.

Данная статья описывает алгоритм оценки непараметрической Марковской модели с помощью плотности копулы Франка. Копульные непараметрические регрессии отличаются тем, что исследователь может разделить различные виды (источники) риска, каждый смоделировать отдельно (непараметрические маргинальные распределения и параметрическая копульная функция) и соединить копулой, свободной от маштаба временной зависимостью. В статье был использован финансовый индекс VIX, измеряющий 30-дневную будущую внутреннюю волатильность на основе индекса акций S & P 500. Этот индекс рассчитывается, исходя из цен опционов. Описанный подход позволяет оценить параметры копулы Франка, правильность выбора которой устанавливается с помощью статистических критериев и является лучшим для данных индекса VIX. То есть эта копула лучше остальных копул описывает историческую зависимость. Далее, на основе функции плотности Франка копулы, был описан механизм оценки коэффициентов непараметрической Марковской регрессии. Такая оценка параметров трудоёмка - нет аналитического решения (параметрический интеграл расходится в точке 0). Таким образом, вычисление параметров происходит с использованием численных методов в пакетах Matlab и Mathematica. Проверить правильность подхода позволяют графические иллюстрации, где можно видеть, что второй момент, добавленный к уравнению, является нелинейным. В результате, используя описанную методологию, можно имитировать индекс VIX в разные промежутки времени и полученные результаты использовать в управлении финансовыми рисками (операции хеджирования через опционы) или принятии спекулятивных торговых позиций с опционами.

This article is dedicated for Fractal Brownian process analysis using Continuous Wavelet Transform (Direct and Inverse). Wavelet Analysis of stochastic processes is very important for financial time series analysis, risk estimation and financial time series forecasting. Wavelet Analysis is very precious for scalability analysis, because of its ability to analyze the signal (process) in scaling and shifting dimensions. In current research, Fractal Brownian motion is analyzed using Direct and Inverse Continuous Wavelet Transform, wavelet coefficients probability density function is estimated, wavelet coefficients lower and upper bounds are calculated using Mexican hat mother wavelet function. At the end estimation results are illustrated.