Igor Melicherčík

Igor Melicherčík
Comenius University Bratislava · Department of Applied Mathematics and Statistics

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17
Publications
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63
Citations
Introduction
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Publications

Publications (17)
Article
Full-text available
We present a dynamic model for optimal investment decisions in defined contribution pension plans. The model determines an optimal fraction of pensioner's savings to be invested in an equity fund, with the rest invested in a bond fund. Since it is dificult to estimate the model parameters exactly, we present sensitivity analysis with respect to var...
Article
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 a...
Article
We present a dynamic model for optimal investment decisions in privately managed defined contribution (DC) pension plans. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modelled by means of the Cox-Ingersoll-Ross model (CIR). The model determines an optimal fraction of pensioner's savings (in time) to be...
Article
In this review paper we recall a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. The model has been proposed and analyzed by the authors. We assume stock prices to be driven by a geometric Brownian motion whereas interest rates are modeled by means of...
Article
Full-text available
We propose a dynamic stochastic accumulation model for determining optimal decision between stock and bond investments during accumulation of pension savings. Stock prices are assumed to be driven by the geometric Brownian motion. Interest rates are modeled by means of the Cox-Ingersoll-Ross model. The optimal decision as a solution to the correspo...
Article
Full-text available
Traditional fire-risk rating indices are founded on statistical relations between pre-event meteorological conditions and the number of fire outbreaks observed in a forested area. However, traditional weather-based indices cannot render information on the spatial distribution of fire-susceptible sites over extensive forested areas because their onl...
Article
Full-text available
Since January 2005, pensions in Slovakia are operated by a three-pillar sys-tem. This paper concentrates on the mandatory, fully funded second pillar. In our analysis we follow the dynamic stochastic accumulation model proposed by the authors in (Kilianovd et al., 2006). Recently pension asset managers tend to be very cautious and they hold low sto...
Article
Full-text available
Risks Due to Variability of K-Day Extreme Precipitation Totals and Other K-Day Extreme Events 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 car...
Article
We present a multistage model for allocation of financial resources to bond indices in different currencies. The model was tested on historical data of interest and exchange rates. We compare a two-stage and a three-stage stochastic programming model from a financial performance point of view.For solving two-stage and three-stage stochastic program...
Article
Since January 2005, pensions in Slovakia are operated by a three-pillar system proposed by the World Bank. The paper discusses and mathematically captures principles of the pension reform in Slovakia. We also discuss the impact of the reform on the deficit of the pension system. We mainly focus on the mandatory, fully funded second pillar. We prese...
Article
Full-text available
Since January 2005, pensions in Slovakia are operated by a three-pillar system as proposed by the World Bank. This paper concentrates on the mandatory, fully funded second pillar. The authors present a dynamic accumulation model for determining the optimal switching strategy among pension funds with different risk profiles. The resulting strategies...
Article
Full-text available
This paper considers two aspects of a recent pension reform in Slovakia: the financial balance of the former pay-as-you-go system, and the level of retirement pensions in a newly introduced two-pillar system. Generally, there are three important steps to sustainable pension reform: a change of pension indexation, a raised retirement age, and the la...
Conference Paper
This chapter describes an algorithm for solving a three-stage stochastic linear program based on the Birge and Qi factorization of a constraint matrix product in the frame of the primaldual path-following interior point method. The algorithm is scalable and enables to solve large linear programs raising from the portfolio management problems. The p...
Article
Full-text available
Fire-risk rating indices are usually based on empirical relationships between pre-event meteorological conditions and the number of observed fire outbreaks. The inherent property of such weather-based indices is that they provide only an area-averaged risk of fire for a given region. This disadvantage can be partially relieved by using remote sensi...
Article
Full-text available
Problems of portfolio management can be viewed as multi-period dynamic decision problems. We present a model for allocation of financial resources to bond indices in different currencies. The future uncertainty is represented by stochastic scenario trees, where stochastic properties of possible future development of exchange rates and interest rate...
Article
We present a multi-state model for allocation of financial resources to bond indices in different currencies. The model is tested on historical data of interest and exchange rates. We compare a two-stage and a three-stage stochastic programming model from the point of view financial performance. Both models are tested using a scenario tree with the...

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