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EN
We deal with the finite complete arbitrage free financial market model. There are given a liability ( as selling an european option) and an initial amount lower than the initial value of the liability. The quantile hedging is based upon the generalized Neyman- Pearson lemma, but this approach don't give all information on the optimal solution in the considered case. In the present paper the optimal randomized test is analysed with some methods of the mathematical programming. It is showed that the minimal generalized density of probabilities equals the needed lower quantil. Moreover we construct the optimal solutions set. It is the basis to formulate the sufficient condition of the classical quantile hedging.
PL
W artykule ukazano analizę wpływu wprowadzonych w Polsce zmian Ustawy o podatku dochodowym od osób fizycznych na proces planowania podatkowego działalności transgranicznej. W rozważaniach uwzględniono także program Rodzina 500+, ponieważ zasiłki na dzieci w większości krajów europejskich stanowią integralną część ich systemów podatkowych. Analizę poprowadzono na przykładzie działalności gospodarczej prowadzonej na terenie Polski oraz Niemiec, co zarówno z metodycznego, jak również praktycznego punktu widzenia wydaje się w pełni uzasadnione. Głównym narzędziem zastosowanym przez autorów były metody całkowitoliczbowego i nieliniowego programowania matematycznego. Do obliczeń wykorzystano oprogramowanie Matematica 9.0, a w niektórych przypadkach moduły stworzone przez autorów.
EN
In the article, the analysis of the influence of introduced in Poland, changes of the Act on Personal Income Tax on the process of tax planning of the transnational activity, was analysed. The considerations also included the Rodzina 500+ Programme because child benefits in most European countries are the integral part of their tax systems. The analysis was conducted on the example of the business activity run on the areas of Poland and Germany, which seems to be justified from both methodological and practical point of view. The main tool, used by the authors, were the methods of integer and non-linear mathematical programming. The calculations were performed in the Mathematica 9.0 software and, in some cases, in the modules created by the authors.
EN
Financial frauds lead to the disturbance of a normal development of stock markets. When they appear, the funds are not properly allocated, which has a negative impact on economic growth. In most cases, investors make decisions taking into consideration economic information presented by companies. Financial frauds substantially affect data included in financial statements. For this reason, it seems important to undertake steps aiming at fraud detection. A key role in this issue may be assumed by auditors who are responsible for identifying significant financial irregularities.
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