a b s t r a c t Dhaene, Denuit, Goovaerts, Kaas and Vyncke [Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R., Vyncke, D., 2002a. The concept of comonotonicity in actuarial science and finance: theory. Insurance Math. Econom. 31 (1), 3-33; Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R., Vyncke, D., 2002b. The concept of comonotonicity in actuarial science and finance: Applications. Insurance Math. Econom. 31 (2), 133-161] have studied convex bounds for a sum of dependent random variables and applied these to sums of lognormal random variables. In particular, they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In this paper we investigate to which extent their general results on convex bounds can also be applied to sums of log-elliptical random variables which incorporate sums of log-normals as a special case. Firstly, we show that unlike the log-normal case, for general sums of log-ellipticals the convex lower bound does no longer result in closed-form approximations for the different risk measures. Secondly, we demonstrate how instead the weaker stop-loss order can be used to derive such closed-form approximations. We also present numerical examples to show the accuracy of the proposed approximations.

Dollar cost averaging (DCA) is a widely employed investment strategy in financial markets. At the same time it is also well documented that such gradual policy is sub-optimal from the point of view of risk averse decision makers with a fixed investment horizon T > 0. However, an explicit strategy that would be preferred by all risk averse decision makers did not yet appear in the literature. In this paper, we give a novel proof for the suboptimality of DCA when (log) returns are governed by Lévy processes and we construct a dominating strategy explicitly. The optimal strategy we propose is static and consists in purchasing a suitable portfolio of path-independent options. Next, we discuss a market governed by a Brownian motion in more detail. We show that the dominating strategy amounts to setting up a portfolio of power options. We provide evidence that the relative performance of DCA becomes worse in volatile markets, but also give some motivation to support its use. We also analyse DCA in presence of a minimal guarantee, explore the continuous setting and discuss the (non) uniqueness of the dominating strategy.

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The study was tend to checking the possibility of using VR technology to invoke specific emotions on the subject. Literature studies have shown a high probability of obtaining successful results, but so far studies have been based on measurements obtained using specialized, expensive equipment. This study was about to show that obtaining similar results is also possible with usage of low budget solutions. Received results allow to conclude even using the less sophisticated technology, satisfactory results can be gained, which can determine the effect of the image displayed in the goggles on the emotions of the subject.

W dobie globalizacji oraz szybkiego postępu gospodarczego zauważyć można rosnące wymagania klientów względem oferowanych produktów i usług. Aby móc sprostać ich oczekiwaniom firmy szukają innowacyjnych i konkurencyjnych rozwiązań. W związku z tym celem opracowania jest poruszenie problematyki zarządzania projektami w logistyce. Zagadnienie zasługujące na szczególną uwagę z punktu widzenia efektywnego zarządzania we współczesnych przedsiębiorstwach. W opracowaniu przedstawiono znaczenie i cele logistyki. Zwrócono szczególną uwagę na definicję, cechy oraz typologię projektów logistycznych.