CURRICULUM VITAE March, 2015 Nikita Ratanov Contact information Facultad de Econom´ıa Universidad del Rosario, Calle 12c, No. 4-69, Bogot´a,D.C. Colombia; Phone: 57-1-2970200 Ext. 647 Fax: 57-1-3445763 E-mail: [email protected] Home page: http://www.urosario.edu.co/Profesores/Listado-de-profesores ACADEMIC RECORD Position held: 2004- present: Full professor (profesor titular), researcher, Faculty of Economics, Rosario University, Bogot´a,Colombia 2002 - 2003: Professor, Department of Computer Science and Statistics, Simon Bolivar University, Caracas, Venezuela 1999 - 2010: Professor, Chair \Mathematical Methods for Economics", Chelyabinsk State University 1999 - 2002: Professor, Head of Department \Mathematical Methods for Economics", Chelyabinsk State University 1984 - 1999: Associate Professor, Chelyabinsk State University 1980-1983: Post-graduate student, Faculty of Mechanics and Mathemat- ics, Moscow State University (Lomonosov) 1976-1980: Assistant Professor, Associate Professor, Department of Math- ematics, Chelyabinsk State University Degrees: 1976: M. Sc. (Diploma in Mathematics) Moscow State University (Lomonosov) 1984: Ph.D. (Physical and Mathematical Sciences: Mathematical Physics) Moscow State University (Lomonosov) Title of thesis: Stabilization of statistical solutions of hyperbolic equa- tions of the second order Supervisors: Professor M.I.Vishik and Dr. A.I.Komech 1 Examiners: Professor Ildar Ibragimov (Leningrad, now St Petersburg), Professor Nikolai Krylov (Moscow, now in University of Minnesota), Profes- sor Rafail Khasminskii (Moscow, now in Wayne State University, Detroit) 1999: Dr.Sci. (Physical and Mathematical Sciences) Russian Academy of Sciences Title of thesis: Wave Equations and Stochastics Examiners: Professor Ildar Ibragimov (St Petersburg), Professor Robert Minlos (Moscow), Professor Isaac Kac (Yekaterinburg) Journal referee Probability Theory and its Applications Statistics and Probability Letters Journal of Applied Probability International Journal of Stochastic Analysis Lithuanian Mathematical Journal Revista Colombiana de Matem´aticas CONFERENCE ORGANIZATION Organizer of international seminar \Mathematical Modeling of Composite Systems" (1990) SCIENTIFIC GRANTS Russian Foundation for Scientific Research 1996: Russian Foundation for Basic Research No. 96-01-01169 1999: Russian Foundation for Basic Research No. 99-01-00989 London Mathematical Society 1997: Visit in Warwick/Cambridge Other research/teaching activities and funding 1995: grant for participation in ICIAM-95 (Hamburg) 1996: Grant of G.Soros foundation 1999: grant for participation in the Second Nordic-Russian Symposium on Stochastic Analysis in Beitostølen, Norway 2000: Research and teaching visit to University of Bonn and University \La Sapienza" (Rome) 2 2002/2003: Research and teaching visit to University \La Sapienza" (Rome) 1999-2002: International Student Business Competition, Nixdorf-Siemens group \Delta" (organizer and coach of students team, 2001 - third place, 2002 - champion of Russian Federation) 2004: Research visit to University of T¨ubingen(Germany) 2005: Research visit to University of Alberta (Canada) 2006: Research visit to University of Alberta (Canada) 2006: Research visit to University of Missouri (USA) 2006: Research visit to Universities of Cardiff, Leeds, London, Cambridge (UK) 2004, 2005, 2006, 2007, 2009: financial support from National Bank (Banco de la Republica de Colombia) of conference participation ( NoLineal 2004; Stoch. Calculus and its Applications to Quantitative Finance and Elec- trical Engineering, Calgary, Canada, 2005; Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation and Related Problems, Detroit, 2006; ICIAM, Z¨urich, 2007; SPA, Berlin, 2009) 2008: International Conference MAF2008, Mathematical and Statistical Methods for Actuarial Sciences and Finance, Venezia 2008: Research visit to University of Milan (Italy), Politecnico di Torino (Italy), University of Luxembourg Research visit to University of Pernambuco (Brazil) Research visit to University of Minneapolis, University of Texas at Brownsville (USA) 2012: Research visit to University \La Sapienza" (Rome) Languages Russian (native), English and Spanish (fluent) RESEARCH HISTORY AND INTERESTS My research work started in the first half of the 1970s, under supervi- sion Dr. A. I. Komech, at the Chair of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University (Lomonosov). At the same time I began my contacts with Professor M. I. Vishik. These two mathematicians have had the strong influence on my research concentrated at that time on the asymptotical behaviour of statistical solutions to hyper- bolic equations (i.e., solutions with random initial data). In 1985 I began 3 working on mathematical problems of quantum statistical mechanics. In my PhD thesis I have proved that if initial data for a hyperbolic equa- tion are chosen to be random and distributed according to a random field with mixing condition, the solution converges, as time increases, to a Gaus- sian field. This result was established for a wide class of linear hyperbolic equations (with constant and non-constant coefficients), including the stan- dard wave equation. Assertions of that kind are naturally related, on the one hand, to a specific form of the Central Limit Theorem of Probability Theory, and on the other hand, to a complete integrability of the equations under consideration. The proof combines arguments from Theory of Differential Equations, Scattering Theory (including scattering for data with infinite en- ergy) and Probability Theory. Later I have proved similar results for some other classes of differential equations. Another direction of my research of this period, which I only mention briefly in this short note, is related to the problem of describing invariant states for various systems of quantum statistical mechanics by means of C∗- algebras technique. Here, again a complete integrability of the system plays an important role. In my Dr.Sci. Thesis I continued the investigations of stochastic solutions to partial differential equations and their asymptotics. The first part contains the discussion of such problems for linear equations with random coefficients. The methods of the proofs are varied from the case of deterministic coeffi- cients mentioned above, and the limit distributions are already non-Gaussian random fields. The problems related to so-called telegraph random walks in inhomogeneous media are investigated as well. In addition there are cal- culated the probabilities of the distributions of first passage times to these processes. The processes with absorption and reflection are investigated as well. Recently some new results related to such processes on a plane were obtained (joint works with prof. E.Orsingher from the University of Rome \La Sapienza"). The work on branching processes with finite velocities and respective nonlinear hyperbolic systems was in the scope of my interests as well. The convergence to travelling wave solutions was proved. This direction of my research has applications to physical and biological problems. Recently financial market models based on Markov chains are constructed and developed. This field of my scientific activity is based on an idea to change a diffusion in the Black-Scholes model by a random walk with finite velocities. It can be applied to option pricing and optimal investments prob- 4 lems as well as to risk-management of equity-linked life insurance contracts. Now it is the point of my principal research interest. TEACHING EXPERIENCE During my professorship I have the experience in teaching university courses in analysis, probability theory, statistics and mathematical physics. My main interests in this area focus on teaching Probability Theory and Statistics. These lectures are a natural extension of my research in the above areas. Eight years ago I began to teach mathematical economics also, par- ticularly stochastic financial mathematics (for students of mathematical and economics faculties). I published the textbook on this topic (in Russian), the extended, modified and corrected version of this book will be published in Spanish in 2008/09. In 2000 and 2002/2003 I've been the visiting professor of the University \La Sapienza" in Rome (Italy). My teaching duties there consisted of the lectures on stochastic analysis and financial mathematics at the Department of Probability, Statistics and Statistic Applications as well as at the Department of Actuarial and Financial Sciences. During my affiliation to the University Simon Bolivar (2002-03) I taught Probability Theory (for undergraduate students) and Applied Probability (for postgraduates). In Colombia (beginning from 2004) I have the experi- ence on teaching of Mathematics for Finance, including stochastic analysis (for undergraduate students of Economics Faculty), Stochastic Analysis and Mathematical Economics (for postgraduates). 5 LIST OF PUBLICATIONS Nikita Ratanov Monograph: Kolesnik, A., RATANOV, N.: Telegraph processes and option pricing. Springer Briefs in Statistics, 2013. Textbooks: 1. RATANOV N. E. Hedging Strategies. Principles of mathematical mod- elling. Textbook for students in economics and applied mathematics, 2001, 187 p. Chelyabinsk State University, Russia, in Russian 2. RATANOV N. Modelos estoc´asticosde mercados financieros. Text- book for students in economics and applied mathematics, 2009, 148 p. University of Rosario, Colombia, in Spanish Refereed journal papers: 1. 2. Ratanov N. Option pricing under