Nenad Šuvak

Associate Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia
phone: +385-31-224-821
fax: +385-31-224-801
email: nsuvak @ mathos.hr
office: 18 (first floor)

 

 


Research Interests

Diffusion processes
Statistical analysis of stochastic processes

Degrees

PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2010
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2004
 

Publications

Google Scholar

Journal Publications

  1. N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli (2017), prihvaćen za objavljivanje
    Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model and Wright-Fisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with non-independent increments. The waiting times are selected from the domain of attraction of a stable law.
  2. N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications 127/11 (2017), 3512-3535
    We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non- Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
  3. I. Tolić, K. Miličević, N. Šuvak, I. Biondić, Non-linear Least Squares and Maximum Likelihood Estimation of Probability Density Function of Cross-Border Transmission Losses, IEEE Transactions on Power Systems (2017), prihvaćen za objavljivanje
    In the modern power system, transmission losses play an increasingly important role in determining the costs of transmission system operators, in particular in cross-border energy exchange. A variety of transmission losses calculation methods are present in scientific literature in recent years, but regularly neglecting the measurement uncertainty which is an important contribution in calculating the final cost of exchanged energy. Due to the significant cost of transmission losses in total costs, all transmission system operators are interested in discovering the probabilistic nature of transmission losses as a fundamental requirement for finding the fair method for transmission losses allocation. In this paper, transmission losses are simulated on 110 kV cross-border transmission line using an Adaptive Monte Carlo method. The probability density estimation procedure is performed by the non-linear least-squares method, using the Levenberg–Marquardt algorithm. The Gaussian, log-normal, Rayleigh, four-parameter beta, generalized trapezoidal and the sum of uniform and normal distribution are fitted and the quality of the distribution estimates is compared according to the corresponding values of the Kolmogorov-Smirnov statistic. Furthermore, an additional example presents a distribution fitting procedure on the zero-impedance data of the same transmission line.
  4. M. Janković, A. Leko, N. Šuvak, Application of lactation models on dairy cow farms, Croatian Operational Research Review 7/2 (2016), 217-227
    One of the most important parts of the contemporary global economy is the food production. Our focus is the milk production on farms of dairy cows, the period in which the cows produce milk (lactation) and the quantity of the milk produced. The special attention will be given to the time-dependent function that describes the quantity of the milk produced over the lactation period. Its graph is known as the lactation curve and it is one of the most important indicators in the dairy farm management. In this paper, we present the time-dependent parametric models for the daily average milk production on one dairy farm. Beside with the well-known Wood's model, the data will be fitted to some less known models such as the MilkBot model and also to the combination of these two models. Model parameters will be interpreted in the framework of the milk production. Finally, we will compare all of the observed models.
  5. D. Grahovac, N. Šuvak, Heavy-tailed modeling of CROBEX, Financial Theory and Practice 39/4 (2015), 411-430
    Classical continuous-time stochastic models for log-returns of risky assets, such as the Black-Scholes model, usually assume independence and normality of distributions of log-returns. However, empirical properties of log-returns often show a specific correlation structure and a deviation from normality, in most cases suggesting that their distribution exhibits heavy tails. A natural alternative for modeling log-returns in continuous time would be a stochastic process incorporating a weak form of dependence and a heavy-tailed distribution that is in some way close to the normal distribution. The Student's distribution with small value of tail index (number of degrees of freedom) is the logical choice for such heavy-tailed distribution. Therefore we suggest an alternative continuous-time model for log-returns, a diffusion process with Student's marginal distributions and exponentially decaying autocorrelation structure. This model depends on several unknown parameters that need to be estimated. The tail index is estimated by the method based on the empirical scaling function, while the parameters describing the mean, the variance and the correlation structure of the model are estimated by the generalized method of moments. The model is applied to the CROBEX stock market index, meaning that the estimation of model parameters is based on the CROBEX log-returns. Quality of the proposed model is assessed by the means of simulations, specifically by comparing CROBEX log-returns with the simulated trajectories of the Student's diffusion depending on estimated parameter values.





Projects

Participation (as researcher) in work of the following projects:

  • Stochastic models with long-range dependence (Stohastički modeli s dugoročnom zavisnošću; 2017-2018), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
  • Fractional Pearson Diffusions (Frakcionalne Pearsonove difuzije; 2015-2016), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
  • Statistical Aspects of Parameter Estimation in Nonlinear Parametric Models (Statistički aspekti procjene parametara u nelinearnim parametarskim modelima; 2007-2013), Department of Mathematic, University of Osijek, Leader: Prof. M. Benšić (the project was funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
  • Models for Risk Assessment of the Company (Modeli za ocjenu rizičnosti poslovanja poduzeća; 2007-2013), Faculty of Economics, University of Osijek, Leader: Prof. N. Šarlija (the project was funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
  • Statistical Analysis of Diffusion Processes and their Applications in Economics and Finance (2009-2010) - this project was a collaborative project with Professor Nikolai N. Leonenko from School of Mathematics, Cardiff University, UK (the project was funded by the Croatian Science Foundation within the program for education of PhD students)

 


 

Grants

  • ERASMUS grant for mobility of scientists (study visit to Babes-Bolyai University, Cluj-Napoca, Romania, 2016)
  • ERASMUS grant for mobility of scientists (study visit to School of Mathematics, Cardiff University, UK, 2013)
  • Grant of the AMAC-UK, United Kingdom Association of Alumni and Friends of Croatian Universities (study visit to School of Mathematics, Cardiff University, UK, 2011)
  • Grant of the Croatian Ministry of Science, Education and Sports for specialization of croatian PhD students at the foreign Universities (study visit to School of Mathematics, Cardiff University, UK, 2008)

 


Professional Activities

Committee Memberships

  • "Innovative Teaching of Mathematics" - National Meeting of Math Teachers, 25-26 August 2016, Osijek, Croatia
    • Chair of the Organizing Committee/Scientific Program Committee
  • 18th European Young Statisticians Meeting, 26-30 August 2013, Osijek, Croatia
    • Chair of the Local Organizing Committee
  • 17th European Young Statisticians Meeting, 5-9 September 2011, Lisbon, Portugal
    • Member of the International Organizing Committee/Scientific Program Committee

Refereeing

  • Mathematical Communications, Random Operators and Stochastic Equations, Journal of Classical Analysis, International Journal of Stochastic Analysis
  • Osijek Mathematical Gazette

Reviewing

  • AMS Mathematical Reviews (since 2011)

 Conferences and Workshops


Lectures and Seminar talks

  • Stohastički integral i Itova formula, Seminar za teoriju vjerojatnosti, PMF-Matematički odjel, Zagreb, 2. i 9. svibnja 2006.
  • Dokazi nepotpunosti bez dijagonalne leme, Seminar za logiku i osnove matematike, PMF-Matematički odjel, Zagreb, 3. travnja 2007.
  • Statistical analysis of Pearson diffusions with heavy-tailed marginal distributions, OR and Statistics Seminar, School of Mathematics, Cardiff University, UK, November 10, 2009
  • Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove, Seminar za optimizaciju i primjene, Odjel za matematiku, Osijek, 16. prosinca 2009.
  • Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove I, II, III, Seminar za teoriju vjerojatnosti, PMF-Matematički odjel, Zagreb, 16. i 23. veljače, 30. ožujka 2010.
  • Testiranje hipoteza za Fisher-Snedecorovu difuziju, Matematički kolokvij, Odjel za matematiku, Osijek, 19. travnja 2012.

Study visits

  • School of Mathematics, Cardiff University, UK (study visits lasting 2-6 weeks in 2007, 2008, 2009, 2010, 2011, 2012, 2013 and 2016)

 Service Activities

  • President of the Osijek Mathematical Society (since 2017)
  • Member of the Higher Education Quality Assurance Board at the Department of Mathematics (since 2006)

Teaching

Konzultacije (Office Hours):

  • Utorkom u 14:00 sati u kabinetu 18 (na katu).

Teme diplomskih radova (akademska godina 2017./2018.)

Courses:

  • Vjerojatnost (Probability), Department of Mathematics, University of Osijek (winter semester)
  • Slučajni procesi (Stohastic Processes), Department of Mathematics, University of Osijek (spring semester)
  • Matematičke financije (Mathematical Finance), Department of Mathematics, University of Osijek (spring semester)
  • Stručna praksa (Professional practice), Department of Mathematics, University of Osijek

Courses taught:

  • StatLab, Elementary Mathematics I and II, Introduction to Probability and Statistics, Introduction to Computer Science, Web Programming (Department of Mathematics, University of Osijek)
  • Mathematics IV (Department of Physics, University of Osijek)
  • Statistics (Faculty of Education, University of Osijek)
  • Mathematics (Faculty of Agriculture, University of Osijek)
  • Probability and Statistics (Faculty of Civil Engineering,  University of Osijek)
  • Statistics (Faculty of Food Technology, University of Osijek)