Discrete copulas and quasi-copulasIvanova, Lina (Avtor) Stopar, Nik (Mentor) copulaquasi-copulabistochastic measurebistochastic matrixThe thesis gives a brief introduction to two dimensional copulas and related functions. Firstly, we present copulas, their usage and according history. Furthermore, in the text we include some examples and visual representations for this purpose. Copulas are cumulative distribution functions defined on the unit square with marginal distributions which are uniformly distributed on the unit interval. The motivation for this topic comes from the fact that this functions are used for describing dependency structures and they represent better tool for this because of the non-linear nature of the variables. Historically, copulas were introduced in the late 50s and quasi-copulas in the 90s which makes them relatively new concept in mathematics with high potential for further analysis. Moreover, after the 90s they got quite popular in the finance world and still today are used in risk management and while modelling returns. An important property of copulas is that they are closely connected to measure theory. Namely, every copula induces a bistochastic measure on the Borel sigma algebra of the unit square and vice versa every bistochastic measure corresponds to some copula. Hence, these functions are measuring something and can be seen as an assignment of a number between 0 and 1 to every rectangle in the unit square. If one discretises the domain of such a function then one can get the so called discrete copulas, which are functions that satisfies similar properties as copulas. They are often useful because it is easier to operate with them. It is possible to construct a copula with discrete copula by extending it from discrete domain to a continuous via piecewise bilinear interpolation. In the last part of the thesis we consider quasi-copulas which are more general functions than copulas. Accordingly, they are a functions defined on a same domain as copulas and have some (but not all) of the properties of copulas. Similarly, one can discretise a quasi-copula in order to get a discrete quasi-copula.20222022-09-15 08:15:17Delo diplomskega seminarja/zaključno seminarsko delo/naloga140494sl