The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation (CVaRD) based Sharpe ratio for measuring risk-adjusted performance of a dynamic portfolio. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index and we evaluate and analyze the dependence of the CVaRD-based Sharpe ratio on the utility function and the associated risk aversion level.
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution to the two factors generalized CIR model and we show that the first two terms in the expansion are independent of the variable representing stochastic volatility.
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.