Nenad Šuvak
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia

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
Journal Publications
 N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli 24/4B (2018), 36033627Continuous 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 urnscheme model and WrightFisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with nonindependent increments. The waiting times are selected from the domain of attraction of a stable law.
 I. Tolić, K. Miličević, N. Šuvak, I. Biondić, Nonlinear Least Squares and Maximum Likelihood Estimation of Probability Density Function of CrossBorder Transmission Losses, IEEE Transactions on Power Systems 33/2 (2018), 22302238In the modern power system, transmission losses play an increasingly important role in determining the costs of transmission system operators, in particular in crossborder 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 crossborder transmission line using an Adaptive Monte Carlo method. The probability density estimation procedure is performed by the nonlinear leastsquares method, using the Levenberg–Marquardt algorithm. The Gaussian, lognormal, Rayleigh, fourparameter 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 KolmogorovSmirnov statistic. Furthermore, an additional example presents a distribution fitting procedure on the zeroimpedance data of the same transmission line.
 N. Leonenko, I. Papić, A. Sikorskii, N. Šuvak, Heavytailed fractional Pearson diffusions, Stochastic Processes and their Applications 127/11 (2017), 35123535We define heavytailed fractional reciprocal gamma and FisherSnedecor diffusions by a non Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with spacevarying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and FisherSnedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavytailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and FisherSnedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
 M. Janković, A. Leko, N. Šuvak, Application of lactation models on dairy cow farms, Croatian Operational Research Review 7/2 (2016), 217227One 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 timedependent 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 timedependent parametric models for the daily average milk production on one dairy farm. Beside with the wellknown 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.
 D. Grahovac, N. Šuvak, Heavytailed modeling of CROBEX, Financial Theory and Practice 39/4 (2015), 411430Classical continuoustime stochastic models for logreturns of risky assets, such as the BlackScholes model, usually assume independence and normality of distributions of logreturns. However, empirical properties of logreturns 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 logreturns in continuous time would be a stochastic process incorporating a weak form of dependence and a heavytailed 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 heavytailed distribution. Therefore we suggest an alternative continuoustime model for logreturns, 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 logreturns. Quality of the proposed model is assessed by the means of simulations, specifically by comparing CROBEX logreturns with the simulated trajectories of the Student's diffusion depending on estimated parameter values.
Projects
Participation (as researcher) in work of the following projects:
 RealForAll  Realtime measurements and forecasting for successful prevention and management of seasonal allergies in CroatiaSerbia crossborder region (2017  2019, project ID: HRRS151)
 Stochastic models with longrange dependence (Stohastički modeli s dugoročnom zavisnošću; 20172018), 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; 20152016), 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; 20072013), 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; 20072013), 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 (20092010)  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 BabesBolyai University, ClujNapoca, Romania, 2016)
 ERASMUS grant for mobility of scientists (study visit to School of Mathematics, Cardiff University, UK, 2013)
 Grant of the AMACUK, 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, 3031 August 2018, Osijek, Croatia
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2526 August 2016, Osijek, Croatia
 Chair of the Organizing Committee/Scientific Program Committee
 18th European Young Statisticians Meeting, 2630 August 2013, Osijek, Croatia
 Chair of the Local Organizing Committee
 17th European Young Statisticians Meeting, 59 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
 Functional Analysis IX , June 2005, Dubrovnik, Croatia
 4th Croatian Mathematical Congress, June 17– 21, 2008, Osijek, Croatia (short communication)
 13th Young Statisticians Meeting, October 16–18, 2008, Balatonfured, Hungary (short communication)
 Croatian Quants Day, April 17, 2009, Department of Mathematics, Zagreb
 16th European Young Statisticians Meeting, August 2428, 2009, Bucharest, Romania (short communication)
 Workshop on Modern Interdisciplinary Applications of Powerful Techicques in Statistics (focus on Singular Spectrum Analysis (SSA) method), December 1, 2009, School of Mathematics, Cardiff University, Cardiff, UK
 "HighDimensional Data Analysis in Economics" Workshop, May 1920, 2010, Faculty of Economics, University of Zagreb, Croatia
 Croatian Quants Day, April 9, 2010, Department of Mathematics, Zagreb
 International Symposium on Business and Industrial Statistics, July 5  9, 2010, Portorose, Slovenia (invited speaker)
 Summer School in Financial Mathematics, August 22  September 2, 2011, Ljubljana, Slovenia
 Statistical Analysis of Financial Data Workshop, September 30  October 1, 2011, Opatija, Croatia (invited speaker)
 Spring School in Probability, April 2327, 2012, Dubrovnik, Croatia
 Croatian Quants Day, May 11, 2012, Department of Mathematics, Zagreb
 Workshop "Modern Trends in Markov Processes and Queuing Theory", February 15, 2013, Welsh Institute of Mathematical and Computational Sciences, Cardiff, UK (short communication)
 18th European Young Statisticians Meeting, August 2630, 2013, Osijek, Croatia
 Workshop on Quantitative Methods for Insurance and Finance, June 56, 2014, Zagreb, Croatia
 15th International Conference on Operational Research KOI 2014, September 2426, 2014, Osijek, Croatia (short communication)
 38th Conference on Stochastic Processes and their Applications, July 1317, 2015, University of Oxford, UK (short communication)
 6th Croatian Mathematical Congress, June 1417, 2016, Zagreb, Croatia (short communication)
 16th Conference on Operational Research KOI2016, September 2729, 2016, Osijek, Croatia (short communication)
 Mathematics for Big Data, May 31  June 1, 2017, Novi Sad, Serbia
 Korean Croatian Summer Probability Camp, July 36, 2017, Zagreb, Croatia
 39th Conference on Stochastic Processes and their Applications, July 2428, 2017, Moscow, Russia (short communication)
 22nd Young Statisticians Meeting, October 1315, 2017. Zagreb, Croatia
Lectures and Seminar talks
 Stohastički integral i Itova formula, Seminar za teoriju vjerojatnosti, PMFMatematički odjel, Zagreb, 2. i 9. svibnja 2006.
 Dokazi nepotpunosti bez dijagonalne leme, Seminar za logiku i osnove matematike, PMFMatematički odjel, Zagreb, 3. travnja 2007.
 Statistical analysis of Pearson diffusions with heavytailed 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, PMFMatematički odjel, Zagreb, 16. i 23. veljače, 30. ožujka 2010.
 Testiranje hipoteza za FisherSnedecorovu difuziju, Matematički kolokvij, Odjel za matematiku, Osijek, 19. travnja 2012.
 Bertrandov paradoks  nastavni izazovi, Geometrijska škola Stanka Bilinskog, SŠ Isidora Kršnjavoga, Našice, 8. travnja 2017.
 Mjere zavisnosti  svojstva i zamke, Statistički seminar, Odjel za matematiku, Osijek, 14. prosinca 2017.
Study visits
 School of Mathematics, Cardiff University, UK (study visits lasting 26 weeks in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2016 and 2018)
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 11:30 i četvrtkom u 14:30 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)