| Abstract [eng] |
In the final master's thesis we investigate Laplace transforms of heavy-tailed distributions, also describe their approximation methods and their practical application options. We chose to investigate non-negative random variables that are Weibull, Pareto or lognormal distributed. These distributions are very popular in finance and actuarial mathematics. Using definition we assure that these distributions are heav-tailed. Laplace transforms, which do not have a simple analytical expression, are then expressed, and their approximation methods are described in detail according to the literature. Examples of specific Laplace transforms are given. Also, using Matlab program, graphs of them and inverse Laplase transforms are drawn. The principle of constructing copulas, induced by Laplace transforms of heavy-tailed distributions, was demonstrated. |
