| Abstract [eng] |
Past few decades, we observe the growth of interest in heavy-tailed distributions. We could find many reasons for that but amongst the most popular explanations are quick spread of information and communication technologies, increased need for financial models that would better correspond to real issues and constantly growing statistical evidence for their appropriateness in natural sciences. Our main object of study is the tail moment of random variable with heavy-tailed or related distribution. Main results of dissertation improve the results existing in the literature. Under weaker assumptions, we give more precise asymptotic bounds for the tail moment of the sum of possibly dependent, heavy-tailed, real-valued random variables. Main results include novel closure properties of heavy-tailed and related distribution classes. Our research shows that for the tail moment to have property, which defines specific class, it is sufficient for corresponding distribution to belong to the same class, but it is not always necessary. When quantifying random losses of any portfolio or company, various risk measures are employed – Value at Risk (VaR), Conditional Value at Risk (CVaR), Haezendonck–Goovaerts (HG) risk measure among many others. To provide examples of application, we found asymptotic formulas specifically for the Haezendonck–Goovaerts risk measure by employing the main results of our dissertation. |
