Research areas of DAMS


Dynamic portfolio management models

Dynamic portfolio management models

  • Mgr. Soňa Kilianová, PhD.
  • doc. Mgr. Igor Melicherčík, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.
  • doc. RNDr. Mária Trnovská, PhD.
  • Cyril Izuchukwu Udeani

Research in the field of dynamic financial and portfolio management models is primarily focused on dynamic stochastic programming in order to maximize utility due to the dynamically changing weights of individual portfolio components. We use methods based on the solution of the Hamilton-Jacobi-Bellman partial differential equation and its suitable transformations. We propose efficient and stable numerical schemes for solving underlying equations. The results are applied mainly in the field of dynamic optimal management of retirement pension funds.

Selected papers published over the past 10 years

  1. Brunovský, P., Černý, A., Komadel, J.: Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions, European Journal of Operational Research 264(3), 2018, pp. 1159-1171.
  2. S. Kilianová, M. Trnovská: Robust Portfolio Optimization via Hamilton-Jacobi-Bellman Equation, International Journal of Computer Mathematics, Vol. 93, No. 5, 2016, 725-734.
  3. S. Kilianová and D. Ševčovič: A Transformation Method for Solving the Hamilton-Jacobi-Bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem, ANZIAM Journal (55) 2013, 14-38.
  4. N. Ishimura, D. Ševčovič: On traveling wave solutions to a Hamilton-Jacobi-Bellman equation with inequality constraints, Japan Journal of Industrial and Applied Mathematics 30(1) 2013, 51-67.
  5. I. Melicherčík and D. Ševčovič: Dynamic Stochastic Accumulation Model with Application to Pension Savings Management, Yugoslav Journal of Operations Research, 2010 20(1):1-24.

Fluid flow dynamics modelling

Fluid flow dynamics modelling

  • doc. RNDr. Peter Guba, PhD.
  • Mgr. Radoslav Hurtiš
  • Mgr. Martin Chudjak, PhD.

The research is focused on theoretical and computational study of the dynamics of complex fluids and its applications to other areas such as mechanical and chemical engineering, materials science and geophysics. Mathematical aspects of research include the theory of asymptotic scaling and reduction of underlying differential equations, the theory of stability and bifurcations, perturbation and asymptotic methods, and numerical methods for partial differential equations.

Selected papers published over the past 10 years

  1. Guba, P., Worster, M. G., Interactions between steady and oscillatory convection in mushy layers, J. Fluid Mech. 645, 411–434, 2010.
  2. Guba, P., Anderson, D. M., Diffusive and phase change instabilities in a ternary mushy layer, J. Fluid Mech. 760, 634–669, 2014.
  3. Kyselica, J., Guba, P., Forced flow and solidification over a moving substrate, Appl. Math. Model. 40, 31–40, 2016.
  4. Guba, P., Anderson, D. M., Pattern selection in ternary mushy layers, J. Fluid Mech. 825, 853–886, 2017.
  5. Šimkanin, J., Kyselica, J., Guba, P., Inertial effects on thermochemically driven convection and hydromagnetic dynamos in a spherical shell, Geophys. J. Int. 212, 2194–2205, 2018.
  6. Kyselica, J., Guba, P., Hurban, M., Solidification and flow of a binary alloy over a moving substrate, Transp. Porous Med. 121, 419–435, 2018.

Evolution of curves and surfaces

Evolution of curves and surfaces

  • prof. RNDr. Daniel Ševčovič, DrSc.

The research is focused on qualitative and numerical aspects in the field of the dynamics modeling of curvature driven flows of plane closed curves. We also focus on the study of various nonlocal geometric flows preserving geometric quantities, such as area or length. Special attention is paid to the design of numerical schemes that are optimal in terms of discretization points distribution on evolving varieties. Finally, we study applications in the field of phase interface dynamics and dislocation loops in materials research.

Selected papers published over the past 10 years

  1. M. Remešíková, K. Mikula, P. Sarkoci and D. Ševčovič: Manifold evolution with tangential redistribution of points, SIAM J. Sci. Comput. 36-4 (2014), A1384-A1414.
  2. M. Kolář, M. Beneš, D. Ševčovič: Area Preserving Geodesic Curvature Driven Flow of Closed Curves on a Surface, Discrete and Continuous Dynamical Systems - Series B, 22(10) 2017, 3671-3689.
  3. D. Ševčovič and S.Yazaki: Computational and qualitative aspects of motion of plane curves with a curvature adjusted tangential velocity, Mathematical Methods in the Applied Sciences, 35(15) (2012), 1784-1798.
  4. M. Kolář, M. Beneš, D. Ševčovič: Computational Analysis of the Conserved Mean-Curvature Flow for Open and Closed Curves in the Plane, Mathematics and Computers in Simulation, 126 2016, 1-13.
  5. D. Ševčovič and S.Yazaki: Evolution of plane curves with a curvature adjusted tangential velocity, Japan J. Indust. Appl. Math., 28(3) (2011), 413-442.
  6. K. Mikula, D. Ševčovič, M. Balažovjech: A simple, fast and stabilized flowing finite volume method for solving general curve evolution equations, Commun. Comput. Phys., 7(1) (2010), 195-211.
  7. V. Klement, T. Oberhuber and D. Ševčovič: Application of the level-set model with constraints in image segmentation, Numerical Mathematics, Theory, Methods and Applications, 9(1) 2016, 147-168.

Qualitative theory of elliptic and parabolic partial differential equations

Qualitative properties of solutions of elliptic and parabolic equations

  • prof. RNDr. Marek Fila, DrSc.
  • Mgr. Petra Macková
  • prof. RNDr. Pavol Quittner, DrSc.

The research is focused on the study of properties of solutions of nonlinear diffusion equations and systems, as well as problems with nonlinear and dynamical boundary conditions. Besides questions related to the existence and uniqueness, we investigate mainly asymptotic properties of solutions.

Selected papers published over the past 10 years
  1. M. Fila, J. L. Vázquez, M. Winkler, E. Yanagida: Rate of convergence to Barenblatt profiles for the fast diffusion equation, Archive Rational Mech. Anal. 204 (2012), 599-625
  2. M. Fila, M. Winkler: Rate of convergence to separable solutions of the fast diffusion equation, Israel J. Math. 213 (2016).
  3. M. Fila, M. Winkler: Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation, Proc. Royal Soc. Edinburgh A 146 (2016), 309-324.
  4. M. Fila, K. Ishige, T. Kawakami: Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition, J. Math. Pures Appl. 105 (2016), 788-809.
  5. M. Fila, M. Winkler: Slow growth of solutions of superfast diffusion equations with unbounded initial data, J. London Math. Soc. 95 (2017), 659-683.
  6. M. Fila, M. Winkler: A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation, Adv. Math. 357 (2019), Art. No. 106823.
  7. T. Bartsch, P. Poláčik, P. Quittner: Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations, J. European Math. Soc. 13 (2011), 219-247.
  8. P. Quittner, Ph. Souplet: Symmetry of components for semilinear elliptic systems, SIAM J. Math. Anal. 44 (2012), 2545-2559.
  9. P. Quittner: Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure, Math. Ann. 364 (2016), 269-292.
  10. P. Quittner, Ph. Souplet: Superlinear Parabolic Problems. Blow-up, Global Existence and Steady States, Birkhäuser Advanced Texts, Birkhäuser, Cham 2019, Second (revised and expanded) edition.

Conic programming and applications

Conic programming and applications

  • Mgr. Terézia Fulová
  • doc. RNDr. Margaréta Halická, CSc.
  • Mgr. Jakub Hrdina
  • Mgr. Soňa Kilianová, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.
  • doc. RNDr. Mária Trnovská, PhD.

The aim of the research is to provide qualitative and numerical analysis of solutions of direct and inverse variational problems, which can be solved using modern methods of conic programming. We focus on the analysis of of strong duality properties of primal and dual pairs in case of conic programming problems.

Selected papers published over the past 10 years

  1. M. Halická, P. Jurča: On the sustainable growth in an economy with perfectly substituable exhaustible resources, Natural Resource Modeling 26 (2013), No 3, 403-434.
  2. M. Halická, M. Trnovská, The Russell measure model: Computational aspects, duality, and profit efficiency, European Journal of Operational Research, 268(1), 2018, 386-397.
  3. Halická, M., Trnovská, M.: Limiting behaviour and analyticity of weighted central paths in semidefinite programming, Optimization Methods and Software, 25(2), 2010, 247-262.
  4. D. Ševčovič and M. Trnovská: Solution to the Inverse Wulff Problem by Means of the Enhanced Semidefinite Relaxation Method, Journal of Inverse and III-posed Problems 23(3) 2015, 263-285.
  5. D. Ševčovič and M. Trnovská: Application of the Enhanced Semidefinite Relaxation Method to Construction of the Optimal Anisotropy Function, IAENG International Journal of Applied Mathematics 45(3) (2015), 227-234.
  6. S. Pavlíková, D. Ševčovič: On a Construction of Integrally Invertible Graphs and their Spectral Properties, Linear Algebra and its Applications, 532 (2017), 512-533.
  7. S. Pavlíková, D. Ševčovič: Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program, Computer Methods in Materials Science, 4 2016, 169-176.

Mathematical modelling of gene expression

Mathematical modelling of gene expression

  • doc. Mgr. Pavol Bokes, PhD.
  • Candan Çelik
  • Mgr. Iryna Zabaikina

Gene expression is a set of processes by which the information encoded in a genetic template is used to make active molecules, especially proteins. The development of new technologies enabling the measurement of gene expression at the level of individual molecules continually motivates the research of mathematical models describing the gene expression dynamics. At our department, we primarily focus on the methodology using differential equations and stochastic simulations.

Selected papers published over the past 10 years

  1. Bokes, P., King, J. R., Wood, A. T., & Loose, M. (2012). Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression. Journal of mathematical biology, 64(5), 829-854.
  2. Singh, A., & Bokes, P. (2012). Consequences of mRNA transport on stochastic variability in protein levels. Biophysical journal, 103(5), 1087-1096.
  3. Bokes, P., King, J. R., Wood, A. T., & Loose, M. (2013). Transcriptional bursting diversifies the behaviour of a toggle switch: hybrid simulation of stochastic gene expression. Bulletin of mathematical biology, 75(2), 351-371.
  4. Soltani, M., Bokes, P., Fox, Z., & Singh, A. (2015). Nonspecific transcription factor binding can reduce noise in the expression of downstream proteins. Physical biology, 12(5), 055002.
  5. Bokes, P., & King, J. R. (2019). Limit-cycle oscillatory coexpression of cross-inhibitory transcription factors: a model mechanism for lineage promiscuity. Mathematical Medicine and Biology: A Journal of the IMA 36(1), 113–137.

Mathematical modelling of the spread of infectious diseases

Mathematical modelling of the spread of infectious diseases

  • Mgr. Peter Barančok
  • doc. Mgr. Pavol Bokes, PhD.
  • Mgr. Ján Gašper
  • doc. Mgr. Radoslav Harman, PhD.
  • Dr. Zuzana Chladná
  • Mgr. Soňa Kilianová, PhD.
  • doc. Mgr. Richard Kollár, PhD.
  • Mgr. Ján Somorčík, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.

The aim of the research is to estimate the public health impact of changes in vaccination indicators on the epidemiological situation. In our research, we focus on highly contagious diseases and their epidemic threats in EU countries. We pay particular attention to two main indicators of vaccination: the vaccination rates and the timeliness of vaccination. Using mathematical and statistical models, we investigate several possible vaccination scenarios and then we evaluate their public health, social and economic impact. We also forecast the epidemiological situation using deterministic and stochastic models and measure the social impact on individuals and society through QALY and DALY indicators.

Selected papers published over the past 10 years

  1. Chladná, Z: Optimal time to intervene: The case of measles child immunization, Mathematical Biosciences and Engineering, 2018, 15(1):323-335.
  2. Chladna, Z., Moltchanova, E. (2015). Incentive to vaccinate: A synthesis of two approaches. Acta Mathematica Universitatis Comenianae, 84(2), 283-296.
  3. H. Hudečková, D. Ševčovič, et al. (spoluautori Z. Chladná, S. Kilianová, P. Brunovský): Biomatematické modelovanie a vyhodnocovanie indikátorov ochorení preventabilných očkovaním, Published by IRIS – Vydavateľstvo a tlač, s.r.o., Bratislava, Slovakia, 2017, 180 pp., ISBN 978-80-8200-002-6.
  4. J. Zibolenová, V. Szabóová, T. Baška, D. Ševčovič, H. Hudečková: Mathematical modeling of varicella spread in Slovakia, Central European Journal of Public Health, 2015; 23 (3): 227-232.
  5. J. Zibolenová, D. Ševčovič, T. Baška, D. Rošková, E. Malobická, V. Szabóová, V. Švihrová, H. Hudečková: Matematické modelovanie infekčných ochorení detského veku, Česko-Slovenská pediatrie, 70(4) 2015, 210-214.

Models of evolutionary genetics, cell biology and animal physiology

Models of evolutionary genetics, cell biology and animal physiology

  • doc. Mgr. Richard Kollár, PhD.

Mathematical models in evolutionary genetics, cell biophysics, and animal physiology help to understand the principles of evolution and functionality of biological species on a macroscopic and microscopic scale. In our research, we study telomeric DNA, which is involved in the regulation of cell aging, the population growth in yeast and the regulation of biorhythms under the influence of the external environment. In addition, our research deals with a number of interesting problems on the edge of current mathematical knowledge, which we study thoroughly.

Selected papers published over the past 10 years

  1. R. Kollár, K. Boďová, J. Nosek, Ľ. Tomáška: Mathematical model of alternative mechanism of telomere length maintenance, Physical Review E 89 (2014), No. 3, 032701.
  2. R. Kollár, K. Šišková: Extension and justification of quasi-steady-state approximation for reversible bimolecular binding, Bulletin of Mathematical Biology 77 (2015), No. 7, 1401-1436.
  3. R. Kollár, S. Novak: Existence of Traveling Waves for the Generalized F–KPP Equation, Bulletin of Mathematical Biology 79 (2017), No. 3, 525-559.
  4. S. Novak, R. Kollár: Spatial Gene Frequency Waves Under Genotype-Dependent Dispersal, Genetics 205 (2017), No. 1 , 367-374.

Random dynamical systems

Random dynamical systems

  • doc. RNDr. Katarína Janková, CSc.
  • Mgr. Jozef Kováč, PhD.

Our research is focused on random dynamical systems generated by continuous self-mappings of an interval and their applications, for example, in population dynamics. We are interested in problems concerning complex behavior of these systems. Under certain conditions, the system stabilizes at some kind of equilibrium, hence its behavior is simple in some sense. Other systems may exhibit extremely unstable behavior which can be considered chaotic. For characterization of this complexity, we use notions of chaos known from the theory of discrete dynamical systems.

Selected papers published over the past 10 years

  1. Janková K.: Chaos and stability in some random dynamical systems, Tatra Mt. Math. Publ. 51(1) (2012), 75-82.
  2. Kováč J., Janková K.: Random Dynamical Dystems Generated by Two Allee Maps, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 27(8) (2017), 1750117.
  3. Kováč J., Janková K.: Distributional chaos in random dynamical systems, J. Differ Equ. Appl. 25(4) (2019), 455–480.

Financial derivatives pricing using differential equations

Financial derivatives pricing using differential equations

  • doc. RNDr. Beáta Stehlíková, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.

In the research we focus on the qualitative and numerical analysis of partial differential equations describing the derivative price changes of the underlying assets, such as interest rate derivatives or equities. We pay special attention to asymptotic and perturbation analysis of solutions depending on parameters and model calibrations for real market data. We also examine the problems leading to the solution of complementarity problems and variational inequalities appearing by valuation of American types of derivatives with early exercise.

Selected papers published over the past 10 years

  1. Chernogorova, T., Stehlíková, B.: A Comparison of Asymptotic Analytical Formulae with Finite-Difference Approximations for Pricing Zero Coupon Bond. Numerical Algorithms 59 (4), 2012, pp. 571-588.
  2. Stehlíková, B., Zíková, Z.: Convergence model of interest rates of CKLS type, Kybernetika, Vol. 48, No. 3, (2012), s. 567-586.
  3. Stehlíková, B., Capriotti, L.: An effective approximation for zero-coupon bonds and Arrow-Debreu prices in the Black-Karasinski model, International Journal of Theoretical and Applied Finance, Vol. 17, No. 6 (2014), Art. No. 1450037, s. 1-16.
  4. D. Ševčovič, B. Stehlíková, K. Mikula: Analytical and numerical methods for pricing financial derivatives. Nova Science Publishers, Inc., Hauppauge, 2011. ISBN: 978-1-61728-780-0 (Hardcover), ISBN: 978-1-61761-350-0 (ebook).
  5. M. Grossinho, Y. Kord Faghan, D. Ševčovič: Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function, Asia-Pacific Financial Markets, 24(4) 2017, 291-308.
  6. D. Ševčovič, M. Žitňanská: Analysis of the nonlinear option pricing model under variable transaction costs, Asia-Pacific Financial Markets, 23(2) 2016, 153-174.
  7. K. Ďuriš, Shih-Hau Tan, Choi-Hong Lai, D. Ševčovič: Comparison of the analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations, Computational Methods in Applied Mathematics 16(1) 2016, 35-50.
  8. T. Bokes, D. Ševčovič: Early exercise boundary for American type of floating strike Asian option and its numerical approximation, Applied Mathematical Finance, 18(5) 2011, 367-394.
  9. M. Lauko, D. Ševčovič: Comparison of numerical and analytical approximations of the early exercise boundary of American put options, ANZIAM journal 51, 2010, 430-448.

Optimal design of experiments

D-optimal approximative design of experiment for a cubic regression model on cube

Optimal design of experiments

  • Mgr. Eva Benková
  • Bc. Assa Camara
  • Mgr. Lenka Filová, PhD.
  • doc. Mgr. Radoslav Harman, PhD.
  • prof. RNDr. Andrej Pázman, DrSc.
  • Mgr. Samuel Rosa, PhD.
  • Mgr. Katarína Sternműllerová, PhD.
  • doc. RNDr. Mária Trnovská, PhD.

Optimal design of experiments is a discipline of mathematical statistics that deals with methods of planning of an experiment in order to obtain as much information as possible within specified constraints on available resources, or to ensure the required data quality at the lowest possible cost. The results of the research in this discipline are applicable in empirical sciences, medicine, industry, agriculture, but also, e.g., in population surveys. The founder of the school of optimal design of experiments at FMPI is prof. RNDr. Andrej Pázman, DrSc., who is also one of the leading figures in this field of research from the global perspective.

Selected papers published over the past 10 years

  1. R Harman, A Bachratá, L Filová, Construction of efficient experimental designs under multiple resource constraints, Applied Stochastic Models in Business and Industry 32 (1), 2016, pp. 3-17.
  2. S Rosa, R Harman, Optimal approximate designs for comparison with control in dose-escalation studies, TEST 26 (3), 2017, pp. 638-660.
  3. Pronzato L, Pázman A (2013): Design of Experiments in Nonlinear Models, Springer, New York.
  4. Harman R, Filová L (2014): Computing efficient exact designs of experiments using integer quadratic programming, Computational Statistics & Data Analysis 71, pp. 1159–1167.
  5. Pázman A, Pronzato L (2014): Optimum designs accounting for the global nonlinear behavior of the model. The Annals of Statistics 42, pp. 194-219.
  6. Sagnol G, Harman R (2015) Computing exact D-optimal designs by mixed integer second-order cone programming, Annals of Statistics 43, pp. 2198-2224.

Probability distributions

Probability distributions

  • doc. RNDr. Katarína Janková, CSc.
  • Mgr. Michaela Koščová
  • Mgr. Jozef Kováč, PhD.
  • doc. Mgr. Ján Mačutek, PhD.
  • doc. RNDr. Karol Pastor, CSc.
  • Mgr. Lívia Rosová, PhD.
  • Mgr. Ján Somorčík, PhD.
  • Mgr. Gábor Szűcs, PhD.

Our research is focused on the analysis of special classes of probability distributions. New statistical methods for distributions from these classes are suggested and theoretically characterized, namely, parameter estimations, goodness of fit tests, and parametric and non-parametric statistical inference. This statistical apparatus is then applied to specific problems in metrology, insurance and financial mathematics, linguistics and demography. As a part of the project, computational methods and algorithms are constructed for these statistical procedures.

Selected papers published over the past 10 years

  1. Mačutek, J., Chromý, J., Koščová: Menzerath-Altmann law and prothetic /v/ in spoken Czech. Journal of Quantitative Linguistics, Vol. 26, No. 1, 2019, p. 66-80, ISSN 0929-6174.
  2. Wimmer, G., Mačutek, J., Altmann, G.: Discrete averaged mixing applied to the logarithmic distributions. Mathematica Slovaca, Vol. 66, No. 2, 2016, p. 483-492, ISSN 0139-9918.
  3. Kelih, E., Mačutek, J.: Number of canonical syllable types: A continuous bivariate model. Journal of Quantitative Linguistics, Vol. 20, No. 3, 2013, p. 241-251, ISSN 0929-6174.
  4. Mačutek, J., Wimmer, G.: Evaluating goodness-of-fit of discrete distribution models in quantitative linguistics. Journal of Quantitative Linguistics, Vol. 20, No. 3, 2013, p. 227-240, ISSN 0929-6174.
  5. Minárik, P., Mináriková, D., Szűcs, G., Golian, J.: Public awareness of food and other lifestyle-related factors towards cancer development among adults in Slovakia: a pilot study. Journal of Food and Nutrition Research, Vol. 55, No. 4, 2016, s. 342-351, ISSN 1336-8672.
  6. Szűcs, G.: Parameter estimation methods for recurrent classes of discrete probability distributions. Forum Statisticum Slovacum, Vol. 11, No. 6, 2015, p. 154-159, ISSN 1336-7420.
  7. Radojičić, M., Lazić, B., Kaplar, S., Stanković, R., Obradović, I., Mačutek, J., Leššová, L.: Frequency and length of syllables in Serbian. Glottometrics, No. 45, 2019, p. 114-123, ISSN 1617-8351.
  8. Tóth, R., Somorčík, J.: On a non-parametric confidence interval for the regression slope. METRON - International Journal of Statistics, Vol. 75, No. 3, Spec. Iss., 2017, p. 359-369, ISSN 0026-1424.

Stability in nonlinear systems

Stability in nonlinear systems

  • doc. Mgr. Richard Kollár, PhD.

The stability of solutions of nonlinear differential equations has an important role in many applications in geophysics, astrophysics, materials engineering, fluid flow mechanics, condensed matter physics, evolutionary biology and in many other fields. In addition to identifying stable states, questions about the changes in stability under the influence of system parameter's changes are also important. In the linear approximation, the stability is characterized by the spectrum of the corresponding operator. In our research we focuses on the study of qualitative spectrum changes, especially via the Krein signature, which identifies potentially unstable modes of Hamiltonian systems.

Selected papers published over the past 10 years

  1. R Kollár, Homotopy method for nonlinear eigenvalue pencils with applications, SIAM Journal on Mathematical Analysis 43 (2011), No. 2, 612-633.
  2. R. Kollár, R. L. Pego: Spectral stability of vortices in two-dimensional Bose–Einstein condensates via the Evans function and Krein signature, Applied Mathematics Research eXpress 2012 (2012), No. 1, 1-46.
  3. R. Kollár, P. D. Miller: Graphical Krein Signature Theory and Evans-Krein Functions, SIAM Review 56 (2014), No. 1, 73-123.
  4. R. Kollár, R. Bosák: Index Theorems for Polynomial Pencils, in Nonlinear Physical Systems. Spectral Analysis, Stability and Bifurcations, ISTE London, 2014, p. 177-202.

Pension schemes

Pension schemes

  • Mgr. Tatiana Jašurková
  • Mgr. Soňa Kilianová, PhD.
  • Mgr. Igor Melicherčík, PhD.
  • Mgr. Matúš Padyšák
  • Mgr. Richard Priesol
  • Mgr. Gábor Szűcs, PhD.
  • prof. RNDr. Daniel Ševčovič, DrSc.

In our research team, we primarily focus on the quantitative analysis of pension systems. In the case of the accumulation phase of saving systems, we study various dynamic portfolio management techniques and we also deal with the problem of finding the optimal investment strategy that maximize the future utility of savers. In the decumulation phase of pension schemes, we examine the impact of risk factors on the future old-age annuity benefits and we also analyze other possible payout products. Our goal is to advance research on mathematical modeling of funded pension schemes, develop dynamic control strategies for savings management and publish applicable results for the old-age pension scheme in Slovakia.

Selected papers published over the past 10 years
  1. Cs. Krommerová, I. Melicherčík: Dynamic portfolio optimization with risk management and strategy constraints. Kybernetika, 50(6), (2014), 1032-1048.
  2. I. Melicherčík, G. Szűcs, I. Vilček: Investment Strategies in the Funded Pillar of the Slovak Pension System. Ekonomický časopis, 63(2), (2015), 133-151.
  3. I. Melicherčík, G. Szűcs, I. Vilček: Investment Strategies in Defined-Contribution Pension Schemes. AMUC, 84(2), (2015), 191-204.
  4. J. Šebo, I. Melicherčík, M. Mešťan, I. Králik: Aktívna správa úspor v systéme starobného dôchodkového sporenia, Wolters Kluwer, Bratislava, (2017), ISBN 978-80-8168-692-4.
  5. A. Černý, I. Melicherčík: Simple Explicit Formula for Near-Optimal Stochastic Lifestyling. European Journal of Operational Research, 284, (2020), 769-778.