CURRICULUM VITAE March, 2015 Nikita Ratanov Contact Information

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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 equations 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 Tübingen(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, Zürich, 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 hyperbolic 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 equation 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 energy) 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 coefficients 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 experience 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:

2. Ratanov N. Option pricing under jump-diﬀusion processes with regime switching. Submitted

3. Ratanov N., Di Crescenzo A. On jump-diﬀusion processes with regime switching: martingale approach. Submitted

4. Ratanov N. Double telegraph processes and incomplete market models. In preparation.

5. Ratanov N. On piecewise linear processes. Statistics and Probability Letters, Volume 90, July 2014, 60-67

6 6. Ratanov N. Double telegraph processes and complete market models. Stoch. Anal. Appl., Volume 32, Issue 4, 2014, 555-574 DOI:10.1080/07362994.2014.899914

7. L´opez O., Ratanov N. On the asymmetric telegraph processes. J. Appl. Prob., 51, No.2, 2014

8. Ratanov N. Telegraph processes with random jumps and complete market models. Method. Comput. Appl. Probab., 2013, Published on line

9. Ratanov N. Damped jump-telegraph processes. Statistics and Proba- bility Letters, 83, 2013, 2282-2290

10. L´opez O., Ratanov N. Kac’s rescaling for jump-telegraph processes. Statistics and Probability Letters, 82, 2012, 1768-1776

11. L´opez O., Ratanov N. Option pricing driven by a telegraph process with random jumps. J. Appl. Prob., 49, No. 3, 2012, 838-849

12. Bogachev L., Ratanov N. Occupation time distributions for the telegraph process, Stoch. Proc. Appl., 121, No. 8, 2011, 1816-1844; doi:10.1016/j.spa.2011.03.016

13. Ratanov N. Option pricing model based on a Markov-modulated diﬀu- sion with jumps. Braz. J. Probab. Stat., 24, Number 2, 2010, 413-431

14. Ratanov N. Jump telegraph processes and a volatility smile. Math. Meth. Econ. Fin., 3, 2008, 93-111.

15. Ratanov N., Melnikov A. On ﬁnancial markets based on telegraph processes. Stochastics: An International Journal of Probability and Stochastic Processes 80, No. 2-3, 2008, 247-268, Zbl 1136.91013; http://dx.doi.org/10.1080/17442500701841156 http://taylorandfrancis.metapress.com/openurl.asp? genre =journalissn=1744-2508 Reprinted in IMS Lecture Notes Monograph Series Vol 57A, Stochas- tics: A Festschrift for Priscilla Greenwood Nick Bingham, Igor Es- tigneev, Editors (http://imstat.org/publications/lecnotes.htm)

7 16. Ratanov N. Jump telegraph processes and financial markets with mem- ory. J. Appl. Math. Stoch. Anal., vol. 2007, Article ID 72326, 19 pages, 2007. doi:10.1155/2007/72326, http://dx.doi.org/10.1155/2007/72326 http://www.emis.de/journals/HOA/JAMSA/ http://www.hindawi.com/journals/jamsa/, Zbl pre05255173 17. Ratanov N. A jump telegraph model for option pricing. Quantitative Finance, 7, No 5, 2007, 575-583, http://dx.doi.org/10.1080/14697680600991226 http://www.journalsonline.tandf.co.uk/openurl.asp? genre=journalissn=1469-7688 http://www.tandf.co.uk/journals/titles/14697688.asp Zbl pre05221746. 18. Ratanov N. Telegraph models of financial markets. Rev. Colombiana de Matem., 41, 2007, 247-252. 19. Melnikov A., Ratanov N. Inhomogeneous telegraph processes and their application to financial market modeling. Doklady Mathematics, 75, 2007, No 1, 115-117. 20. Orsingher E., Ratanov N. Exact distributions of random motions in inhomogeneous media. Theory of Probability and Mathematical Statis- tics, 2007, 76, 125-137. 21. Ratanov N. An option pricing model based on jump telegraph processes. Proc. Appl. Math. Mech. (PAMM), Volume 7, Issue 1, pp. 2080009-2080010, DOI 10.14002/pamm.200700351 22. Ratanov N. Branching random motions, non-linear hyperbolic systems and travelling waves. European Series in Applied and Industrial Math- ematics (ESAIM:PS), 2006, 10, 236-257, http://dx.doi.org/10.1051/ps:2006009 http://www.edpsciences.org/journal/index.cfm?edpsname=ps Zbl pre05216857. 23. Ratanov N. Pricing options under telegraph processes. Rev. Econ. Ros., 8(2) 2005, 131-150.

8 24. Ratanov N. Reaction-advection random motions in inhomogeneous media. Physica D: Nonlinear Phenomena. 2004, 189, No.1-2, 130-140, http://dx.doi.org/10.1016/j.physd.2003.09.032 http://www.sciencedirect.com/science/journal/01672789 Zbl 1052.35115.

25. Dudnikova T.V., Komech A.I., Ratanov N.E., Suhov Y.M. On convergence to equilibrium distribution II. The wave equation in odd dimen- sions, with mixing. J. Stat. Phys., 2002, 108, No.5-6, 1219-1254, http://dx.doi.org/10.1023/A:1019755917873 http://www.springerlink.com/openurl.asp?genre=journalissn=0022-4715 Zbl 1071.82004.

26. Orsingher E., Ratanov N. Planar random motions with drift. J. Appl. Math. Stoch. Anal., 2002, 15, No.3, 205-221, http://www.emis.de/journals/HOA/JAMSA/ http://www.hindawi.com/journals/jamsa/ Zbl 1022.60063.

27. Ratanov N.E. Telegraph evolutions in inhomogeneous media. Markov Processes and Related Fields, 1999, 5, No 1, 53-68, http://www.math.msu.su/ malyshev/mprf.htm Zbl 0924.60054.

28. Ratanov N.E. Random walks of a particle in an inhomogeneous one- dimensional environment with reﬂection and absorption. (Russian) Teoret. Mat. Fiz., 1997, 112, N.1, 81-91; translation in Theor. and Math.Phys., 1997, 112, no.1 857-865 (1998), http://dx.doi.org/10.1007/BF02634100 http://www.springerlink.com/openurl.asp?genre=journalissn=0040-5779 Zbl 0978.82508

29. Ratanov N.E. Asymptotic behaviour of the statistical solutions of linear diﬀerential equations. Z. Angew. Math. Mech., 1996, 76, Suppl. 3, 545-546, Zbl 0925.35164

30. Ratanov N.E. On the invariance principle for the solutions of stochastic wave equation. Random Oper. and Stoch. Equations, 1996, 4, No.3, 273-282,

9 http://www.degruyter.de/journals/rose/detail.cfm http://dx.doi.org/10.1515/ROSE, Zbl 0865.60025.

31. Ratanov N.E. On the asymptotics of the statistical solutions of wave equation with variable coeﬃcients. Random Oper. and Stoch. Equa- tions, 1996, 4, No.4, 339-350, http://www.degruyter.de/journals/rose/detail.cfm http://dx.doi.org/10.1515/ROSE, Zbl 0874.35138.

32. Ratanov N.E. On invariant gaussian measures for hyperbolic equation of the second order. (Russian) Vestnik Chelyabinsk. Univ. Ser.3 Mat. Mekh. , No.1 (3), 1996, 90-98.

33. Ratanov N.E., Sukhov Yu.M. Invariant states for the time dynamics of a class of multidimensional lattice quantum Fermi-systems. Teoret. Mat. Fiz., 1993, 94, No.1, 76-83; translation in Theor. and Math. Phys., 1993, 94, no.1, 55-60, http://dx.doi.org/10.1007/BF01016990 http://www.springerlink.com/openurl.asp?genre=journalissn=0040-5779, Zbl 0806.46081.

34. Ratanov N.E., Sukhov Yu.M. Invariant states for time dynamics of one- dimensional lattice quantum Fermi-systems. (Russian) Teoret. Mat. Fiz., 1991, 88, No.2, 247-259; translation in Theor. and Math. Phys., 1991, 88, no.2, 849-858 (1992).

35. Ratanov N.E., Shuhov A.G., Suhov Yu.M. Stabilization of the statistical solution of the parabolic equation. Acta Appl. Math., 1991, 22, 103-115, http://www.springerlink.com/openurl.asp?genre=journalissn=0167-8019, Zbl 0754.60063.

36. Ratanov N.E. Stabilization of space-time statistical solutions of the parabolic equation. (Russian) Vestnik Chelyabinsk. Univ. Ser.3 Mat. Mech., 1991, No.1, 64-71, Zbl 0796.35064.

37. Ratanov N.E. Asymptotic normality of the statistical solutions of the wave equation. Mosc. Univ. Math. Bull., 40, No.4, 77-79 (1985);

10 translation from Vestn. Mosk. Univ., Ser. I 1985, No.4, 73-75 (1985), http://www.springerlink.com/content/0027-1322 Zbl 0588.35045.

38. Ratanov N.E. Stabilization of statistical solutions of second-order hyperbolic equations. Russ. Math. Surv., 39, No.1, 179-180 (1984); translation from Usp. Mat. Nauk 39, No.1(235), 151-152 (1984), http://dx.doi.org/10.1070/RM1984v039n01ABEH003081 http://www.turpion.org/php/homes/pa.phtml?jrnid=rm, Zbl 0567.35051.

Refereed papers in books:

1. Komech A.I., Ratanov N.E. Stabilization of space-time stochastic solutions of wave equation. - In Statistics and Control of Stochastic Pro- cesses, v.2, Steclov Seminar 1985-1986. // Optimization Software Inc., Publication Division, New York-Los Angeles, 1989, pp.171-187, Zbl 0741.60025.

2. Ratanov N.E. On asymptotic normality of the statistical solutions of the wave equation. - In Diﬀerential Equations and Their Applications, Collect. Artic., Moskov. Gos. Univ., 1984, 153-160, Zbl 0588.35046.

3. Ratanov N.E. Stabilization of the statistical solutions of the wave equation. - Ibid, 95-101, Zbl 0582.35067.

Other publications:

1. Ratanov N. Jump Telegraph-Diﬀusion Option Pricing. Universit´adegli Studi di Milano, Paper 33, Berkeley Electronic Press, 2008 (http://services.bepress.com/unimi/statistics/art33)

2. Ratanov N. Quantile hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts. Preprint No. 62 of Rosario University, Bogot´a,Colombia, 2005.

3. Ratanov N. A jump telegraph model for option pricing. Preprint No. 58 of Rosario University, Bogot´a,Colombia, 2004.

11 4. Ratanov N. Option pricing model based on telegraph process with jumps. Preprint No.44 of Rosario University, Bogot´a,Colombia, 2004.

5. Ratanov N. Branching random motions, non-linear hyperbolic systems and travelling waves. Preprint of Simon Bolivar University, Caracas, Venezuela, 2003, 32 p.

6. Orsingher E., Ratanov N. Exact distributions of random motions in inhomogeneous media. Preprint of the University ”La Sapienza”, Rome, Italy, 2003, 15 p.

7. Ratanov N. Russian financial instruments. - In Seminari sul rischio finanziario a.a.1999-2000. A.Freddi (ed). Scientific publications of the University of Rome ”La Sapienza”, 2002, pp. 139-162.

8. Ratanov N. Option pricing models and limits of arbitrage. - In Sem- inari sul rischio ﬁnanziario a.a.1999-2000. A.Freddi (ed). Scientiﬁc publications of the University of Rome ”La Sapienza”, 2002, pp.123- 138.

9. Ratanov N.E. Hedging strategies and limits of arbitrage. - In System Analysis in Economics, Taganrog, Russia, 2001, pp. 87-102.

10. Orsingher E., Ratanov N. Planar random motions with drift. Preprint n. 29 of the University ”La Sapienza”, Rome, Italy, 2000, 17 p.

11. Dudnikova T.V., Komech A.I., Ratanov N.E. On convergence to statistic equilibrium in wave equations with mixing. Preprint of Max-Planck Institute for Mathematics in the Sciences, Leipzig, 2000, 28 p.

12. Ratanov N.E. On the telegraph processes in inhomogeneous media. Preprint University of Warwick, United Kingdom. N36/1997. October 1997. 12 p.

13. Ratanov N.E. An asymptotics of statistical solutions of the wave equation with random coeﬃcient. Preprint University of Warwick (United Kingdom), May 1995, 14 p.

14. Ratanov N.E. Stabilization of the statistical solution to the wave equation. Dep. in VINITI, May 7, 1984, N2912-84 Dep., 24 p.

12 Selected published conference papers

1. Ratanov N.E. Stabilization of statistical solution of hyperbolic equations. // 1st World Congress of the Bernoully Society (USSR, Tashkent, 1986), Abstracts, v.2, Nauka, Moscow, p.831.

2. Ratanov N.E. Stabilization of space-time statistical solutions of wave equation. // Russian Math. Surveys (Uspechi Math. Nauk), 1986, v.41, No.4, pp.161-162 (Conference dedicated to I.Petrovskii, Moscow State University).

3. Ratanov N.Ye. On stabilization of statistical solution of parabolic differential equations. // Abstracts of 5th Vilnius conference on probability theory and mathematical statistics, v.2, USSR, Vilnius, 1989, pp.106-107.

4. Ratanov N.E. Invariant measures of the hyperbolic equations of the second order. // Abstracts of XIY school on theory of operators in functional spaces, part 3, USSR, Novgorod, 1989, p.18 (Russian).

5. Ratanov N.E. On stabilization of solutions of some Cauchy problems. // Abstracts of the 2nd International Seminar ”Nonsmooth and Dis- continuous Problems of Control and Optimization”, Chelyabinsk, 1993, p.118-119.

6. Kometch A.I., Kopylova E.A., Ratanov N.E. The stabilization of statistics in wave and Klein-Gordon equations with mixing. Scattering theory for inﬁnite energy solutions. // Second International Conference on Mathematical and Numerical Aspects of Wave Propagation. - Uni- versity of Delaware, USA, 1993.

7. Komech A.I., Ratanov N.E., Suhov Yu.M. Asymptotic behavior of the statistical solutions of the linear diﬀerential equations. // The Third International Congress of Industrial and Applied Mathematics, Ham- burg, 1995.

8. Ratanov N.E. The asymptotics of statistics in wave equation with random coeﬃcients. // Warwick Symposium on Stochastic Analysis and Related Fields. Warwick, UK, 1995.

13 9. Ratanov N.E. On telegraph procesess in inhomogeneous media. // Second European Congress of Mathematicians. Budapest, 1996.

10. Ratanov N.E. Telegraph Processes with Reﬂectors and Traps in In- homogeneous Media. // Stochastic and Global Analysis, Voronezh, Russia, 1997.

11. Ratanov N.E. Random motions and hyperbolic equations. // 7th Vil- nius Conference on Probability Theory and Mathematical Statistics. Vilnius, 1998.

12. Ratanov N. Telegraph processes and option pricing. // 2nd Nordic- Russian Symposium on Stochastic Analysis, Beitostolen, Norway, 1999.

13. Ratanov N. Telegraph random motions with reﬂections and traps in inhomogeneous media. Stat. Mech. 2000, Satellite meeting of Xiii IAMP, Cambridge, 2000, p.23-24.

14. Ratanov N. Telegraph processes in inhomogeneous media. // The international seminar on geometry and functional analysis dedicated to N.V.Eﬁmov. Abrau-Durso, 2000.

15. Ratanov N. Hedging strategies in complete markets. // The international conference ”System Analysis in Economics”, Gelengik, Russia, 2000.

16. Ratanov N. On non-arbitrage criterion in the Cox-Ross-Rubinstein model. // Review of Industrial and Applied Mathematics, v.7, N2, 2000 (I Congress on Applied and Industrial Mathematics, Sochi, Rus- sia, 2000).

17. Ratanov N. Random walks on a plane driven by hyperbolic equations. // Review of Industrial and Applied Mathematics, v.8, N1, 2001.

18. Ratanov N. Exact distributions of random motions on inhomogeneous plane. // International Conference ”Stochastic Analysis and Related Fields”, St Petersburg, 2001.

19. Ratanov N. Nonlinear telegraph equation, travelling waves and history dependent media // Memorias del VI Congreso Internacional de

14 métodos numéricosen ingenier´ıa y ciencias aplicadas (CIMENICS 2002): Desarrollos recientes en métodos numéricosen ingenier´ıay ciencias aplicadas, Caracas, Venezuela, 2002, pp. AD57-AD64

20. Ratanov N. Branching random motions, nonlinear hyperbolic systems and travelling waves. Movimientos aleatorios con ramificación,sistemas hiperbólicos no lineales y ondas viajeras. // Congress ”NoLineal 2004”, Toledo, Spain, 2004.

21. Ratanov N. Option pricing model based on jump telegraph processes // Stoch. Calculus and its Applications to Quantitative Finance and Electrical Engineering. A conference in honor of the contributions of Robert J. Elliott, Calgary, Canada, 2005

22. Ratanov N. Telegraph models of ﬁnancial markets // XV National Congress of Mathematics, Bogot´a,Colombia, 2005.

23. Ratanov N. Jump telegraph models of ﬁnancial markets // Interna- tional Symposium in Actuarial Sciences, Bogot´a,Colombia, 2006 (in- vited lecture)

24. Ratanov N. Option pricing based on telegraph processes // Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation and Re- lated Problems, Conference in Honor of Rafail Z. Khasminskii on the occasion of his 75th birthday, Detroit, Wayne State University, 2006

25. Ratanov N. A jump telegraph model for option pricing // 6th Interna- tional Congress on Industrial and Applied Mathematics, Z¨urich, 2007

26. Ratanov N. Option pricing model based on jump telegraph processes // International Conference MAF2008, Mathematical and Statistical Methods for Actuarial Sciences and Finance, Venezia, 2008

27. Ratanov N. Option Pricing Model Based on Markov-modulated Pro- cesses with Jumps // XII Escola Brasileira de Probabilidade, Ouro Preto, Brazil, 2008

28. Ratanov N. Markov-modulated jump-diﬀusion processes and option pricing // 33rd Conference on Stochastic Processes and Their Applica- tions, Berlin, Germany, 2009

15 29. Ratanov N. Jump-Telegraph Option Pricing // Fifth General Confer- ence on Advances Mathematical Methods in Finance, Hotel Golf, Bled, Slovenia, May 3 - 9, 2010

30. Ratanov N. Option pricing model based on telegraph processes // Ple- nary lecture, 11th WSEAS International Conference MCBE10, Iasi, Romania, JUNE 13-15, 2010

31. Ratanov N. Random Evolutions and Option Pricing // International Conference on Applied Mathematics and Informatics (ICAMI2010), San Andres, Colombia, 28.11.2010-03.12.2010

32. Ratanov N. Occupation time distributions for the telegraph process // International Conference on Applied Mathematics and Informatics (ICAMI2010), San Andres, Colombia, 28.11.2010-03.12.2010