We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution, the portfolio insurance with spreads.
Several alternative definitions of extreme events are proposed. As the first step a statistical analysis of daily precipitation measurement time series from the Hurbanovo SHMI Observatory and elaboration of potentially dangerous precipitation events is carried out. Then, combined characteristics based on daily temperature, daily air humidity and daily precipitation totals are computed. The drought index based on normalized deviations from long-term averages is defined. Alternatively, to define extreme events ''Data envelopment analysis'' (DEA) is employed with K-day periods of values of temperature, humidity and precipitation corresponding to decision making units. In this paper we have used the period of K = 10 days for both methodologies for identification of extreme events. The results of all definitions of extreme events are compared. and V článku navrhujeme niekoľko definícií extrémnych udalostí. Ako prvý krok je vypracovaná štatistická analýza denných úhrnov zrážok z observatória SHMÚ v Hurbanove, na základe ktorej označujeme extrémne udalosti. Následne počítame kombinované charakteristiky období sucha založené na denných údajoch teploty, vlhkosti vzduchu a denných úhrnoch zrážok. Index sucha je založený na normalizovaných odchýlkach od dlhodobých priemerov. Alternatívne definujeme extrémne udalosti na základe DEA analýzy, kde K-denné periódy teploty, vlhkosti a zrážok slúžia ako rozhodovacie jednotky. V tomto článku sme na identifikáciu extrémnych udalostí pre obe metodológie použili periódu K = 10 dní. Výsledky všetkých prístupov nakoniec porovnávame.