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Zależność: fakty i mity

100%
Heilpern S.
Studia Ekonomiczne
|
2014
|
vol. 207
85-98
PL
Artykuł poświęcony jest wybranym zagadnieniom zależności zmiennych losowych, które można opisać za pomocą funkcji łączących (kopula). Opisano związek dwuwymiarowego rozkładu normalnego z gaussowską funkcją łączącą wraz z najczęściej stosowaną miarą zależności: współczynnikiem korelacji Pearsona. Wnioski odniesiono do przypadku wielowymiarowych rozkładów eliptycznych, w szczególności rozkładów normalnych. Zbadano także rozkład sumy zmiennych losowych pod względem najczęściej stosowanej miary ryzyka, jaką jest VaR. Pokazano, że największe wartości tej miary wcale nie muszą zachodzić dla ścisłej zależności ani dla niezależności.
EN
The main aim of the article is to show chosen issues of random variables which can be described in the form of copula functions. In the first part the relationship between two-dimensional normal distribution with Gaussian copula function was shown together with the most common measure - Pearson correlation coefficient. Conclusions were referred to multivariate elliptical distributions, mainly to normal distributions with major focus on generally used risk measure - value at risk (VaR). It was shown that the highest values of this measure need not appear for close dependence as well as for independence.
2
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Proces ryzyka z zależnymi okresami między wypłatami - analiza prawdopodobieństwa ruiny

100%
Heilpern S.
Studia Ekonomiczne
|
2013
|
vol. 133
7-19
EN
The paper is devoted to the risk process with dependent interclaim times. The influence of degree of dependence of interclaims on the probability of ruin is investigated. The case of the strict dependence and the case when the dependence structure is described by the Archimedean copula is studied. The localization of the extreme values of the probability of ruin essentially depends on the value of initial capital. The most values of the probability of ruin are attain for the middle values of degree of dependence.
3

Estymacja przedziałowa wartości oczekiwanej zmiennej losowej z wykorzystaniem współczynnika asymetrii

75%
Baszczyńska A., Pekasiewicz D.
Wiadomości Statystyczne. The Polish Statistician
|
2007
|
issue nr 7
1-10
XX
W artykule przedstawiono niektóre modyfikacje klasycznego przedziału ufności, wyznaczonego na podstawie centralnego twierdzenia granicznego dla wartości oczekiwanejzmiennej losowej, stosowane w przypadku, gdy zmienna ta ma rozkład asymetryczny. W rozważanych procedurach estymacji przedziałowej wykorzystano informacje o wartości współczynnika asymetrii z populacji lub wartości oszacowanej na podstawie próby. Stosując metody Monte Carlo, zanalizowano efektywność rozpatrywanych procedur estymacji poprzez porównanie długości otrzymywanych przedziałów ufności. Wyznaczano odsetek przedziałów, pokrywających szacowaną wartość oczekiwaną wygenerowanych populacji. Analiza wielkości tego odsetka dla rozkładów asymetrycznych uzasadnia potrzebę modyfikacji klasycznej metody estymacji przedziałowej wartości oczekiwanej zmiennej losowej. (abstrakt oryginalny)
EN
In the article some modifications of classical confidence interval were presented, determined on the base of the central limit theorem for the expected random variable's value, which are used in case of variable with asymmetrical distribution. In the considered procedures of the interval estimation, the information about coefficient ofskewness of population or value estimated on the base of sample was used. By using Monte Carlo method, the efficiency of examined estimation procedure was analyzed by length comparison of received confidence intervals. Intervals interest, which covers estimated expected value of generated populations, was determined. The analysis of this interest rate for asymmetrical distribution proves the need of modification of the classical estimation interval method of expected value of random variable. (original abstract)
4
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Sprawdzanie jednorodności jakości materiałów niekształtnych z wykorzystaniem rozkładów wartości ekstremalnych

75%
Kończak G.
Studia Ekonomiczne
|
2013
|
vol. 152
82-94
EN
For quality control it is essential that the control samples are homogeneous. In practice this is impossible, and the requirement can be reduced to the condition that the samples were taken from the same population. The study presented in the paper is an analysis of the issue of testing the quality of the shapeless material. As a shapeless material is referred to the material from which it is impossible to directly extract the individual elements, packages, etc. This paper proposes a method to verify the hypothesis that the tested material is homogeneous due to the observed characteristics.
5
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Miary zależności - analiza statystyczna na przykładzie wybranych walorów rynku metali nieżelaznych

63%
Krężołek D.
Studia Ekonomiczne
|
2014
|
vol. 192
59-82
EN
The analysis of investment risk is strongly associated with the knowledge of dependency structure between assets. The aim of this paper is to present some dependency and concordance measures between random variables. Such measures as Pearson coefficient of correlation, Kendall's tau and Spearman's rho has been discussed. Moreover, the measures of tail dependencies has been presented. An empirical analysis has been carried out using selected assets from non-ferrous metals market.
6
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Wielowymiarowa warunkowa wartość zagrożona jako miara ryzyka

63%
Krzemienowski A.
Studia Ekonomiczne
|
2013
|
vol. 154
53-60
EN
The Multivariate Conditional Value-at-Risk (MCVaR) is a scalar risk measure for multivariate risks modeled by multivariate random variables. It is assumed that the univariate risk components are perfect substitutes, i.e., they are expressed in the same units. MCVaR is a quantile risk measure that allows one to emphasize the consequences of more pessimistic scenarios. By changing the level of the quantile, the measure permits to parameterize prudent attitudes toward risk ranging from extreme risk aversion to risk neutrality. In terms of definition, MCVaR is slightly different from the popular and well-researched Conditional Value-at-Risk (CVaR). Nevertheless, this small difference allows one to efficiently solve MCVaR portfolio optimization problems based on the full information carried by a multivariate random variable using column generation technique, which is not possible in the case of CVaR.
7
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Ewolucja metod oceny ryzyka rynkowego

63%
Trzpiot G.
Studia Ekonomiczne
|
2014
|
vol. 192
31-43
EN
By experience of the last financial crises new principles of setting reserves in order to secure risky investments were implemented. The security level depends from the type of investment as well as from the accepted measure of the risk. Conventional approach mean-variance isn't appropriate to the present market situation in the description and the inspection of the level of risk, so institutionally appropriately accepted other measures of the risk are proposed. In the article we will present stress VaR and the IRC (Incremental Risk Charge). We will describe the relation additionally between the linear and nonlinear measurement of the risk in connecting with the level of risk and the type the schedule of a random variable describing examined investment.
8
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Związki miar awersji do ryzyka z funkcjami zależnymi od parametrów rozkładu

63%
Kopańska-Bródka D.
Studia Ekonomiczne
|
2013
|
vol. 163
253-266
EN
The expected utility model (EU) and the mean-variance model (M-V) are the most common approaches to analyzing choices under uncertainty. These two models produce the preference relations which are only consistent under additional restrictions. Although the mean-variance preferences has been important in financial economics, such a concept of risk is not consistent with others. However, the decision makers select alternatives by comparing their risk, and various risk measures are employed. The main aim of the paper is to compare various concepts of measure of risk aversion and present some conditions providing consistency in the two approaches.
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