University of Vaasa Department of Mathematics and Statistics
Faculty of Technology

Research

Research interests

Fractional, Gaussian, self-similar, and quadratic variation processes; stochastic analysis; statistics for stochastic processes; stochastic simulation; mathematical finance; financial engineering.

Publications

    Ph.D. thesis

  1. Sottinen, T. (2003) Fractional Brownian motion in finance and queueing. Ph.D. Thesis, University of Helsinki. (items 2, 4, 5, and 6 with an introduction)

    Journals with referee system

  2. Sottinen, T. (2001) Fractional Brownian motion, random walks and binary market models. Finance and Stochastics 5, no. 3, 343-355.
  3. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2002) Self-similar processes with stationary increments in the spaces SSub_\phi(\Omega). Theory of Probability and Mathematical Statistics 65, 77-88 .
  4. Kozachenko, Yu., Vasylyk, O. and Sottinen, T. (2002) Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic. Queueing Systems 42, no. 2, 113-129.
  5. Sottinen, T. and Valkeila, E. (2003) On arbitrage and replication in the Fractional Black-Scholes pricing model. Statistics & Risk Modeling 21, 93-107.
  6. Sottinen, T. (2004) On Gaussian processes equivalent in law to fractional Brownian motion. Journal of Theoretical Probability 17, no. 2, 309-325.
  7. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2005) Simulation of weakly self-similar stationary increment Sub_\phi(\Omega)-processes: a series expansion approach. Methodology and Computing in Applied Probability 7, 379-400.
  8. Sottinen, T. and Tudor, C.A. (2006) On the equivalence of multiparameter Gaussian processes. Journal of Theoretical Probability 19, no. 2., 461-485.
  9. Sottinen, T. and Tudor, C.A. (2008) Parameter estimation for stochastic equations with additive fractional Brownian sheet. Statistical Inference for Stochastic Processes 11, 221-236.
  10. Särkkä, S. and Sottinen, T. (2008) Application of Girsanov Theorem to Particle Filtering of Discretely Observed Continuous-Time Non-Linear Systems. Bayesian Analysis 3, no. 3., 555-584.
  11. Bender, C., Sottinen, T. and Valkeila, E. (2008) Pricing by hedging and no-arbitrage beyond semimartingales. Finance and Stochastics 12, 441-468.
  12. Morlanes, J. I., Rasila, A. and Sottinen, T. (2009) Empirical evidence on arbitrage by changing the stock exchange. Advances and Applications in Statistics, no. 2, Vol. 12, 223-233.
  13. Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2011) Lipschitz conditions for Sub_\phi(\Omega)-processes with application to weakly self-similar stationary increment processes. Theory Probab. Math. Stat. 82, 57-73.
  14. Gapeev, P., Sottinen, T. and Valkeila, E. (2011) Robust replication in H-self-similar Gaussian market models under uncertainty. Statistics & Risk Modeling 28, 37-50.
  15. Gasbarra, D., Sottinen, T., and van Zanten, H. (2011) Conditional full support of Gaussian processes with stationary increments. Journal of Applied Probability 48, No. 2., 561-568.
  16. Sottinen, T. and Yazigi, A. (2014) Generalized Gaussian Bridges. Stochastic Processes and their Applications 124, Issue 9, 3084-3105.
  17. Azmoodeh, E., Sottinen, T., Viitasaari, L. and Yazigi, A. (2014) Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes. Statistics & Probability Letters 94, 230-235.
  18. Azmoodeh, E., Sottinen, T. and Viitasaari, L. (2015) Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model. Modern Stochastics: Theory and Applications, 2, No. 1, 29-49.
  19. Sottinen, T. and Viitasaari, L. (2016) Pathwise integrals and Ito-Tanaka Formula for Gaussian processes. Journal of Theoretical Probability 29, Issue 2, 590-616.
  20. Sottinen, T. and Viitasaari, L. (2016) Stochastic Analysis of Gaussian Processes via Fredholm Representation. International Journal of Stochastic Analysis, doi:10.1155/2016/8694365.
  21. Pakkanen, M.S., Sottinen, T. and Yazigi, A. (2017) On the conditional small ball property of multivariate Levy-driven moving average processes, Stochastic Processes and their Applications, 127, Issue 3, 749-782.
  22. Sottinen, T. and Viitasaari, L. (2017) Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise. Statistical Inference for Stochastic Processes, doi:10.1007/s11203-017-9156-6.
  23. Yang, X., Rasila, A. and Sottinen, T. (2017) Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence. Methodology and Computing in Applied Probability, 19, 589-602.
  24. Sottinen, T. and Viitasaari, L. (2017) Prediction Law of Fractional Brownian Motion. Statistics & Probability Letters 129, 155-166.
  25. Shokrollahi, F. and Sottinen, T. (2017) Hedging in fractional Black-Scholes model with transaction costs. Statistics & Probability Letters 130, 85-91.

    Proceedings with referee system

  26. Gilsing, H. and Sottinen, T. (2003) Power series expansions for fractional Brownian motions. Theory of Stochastic Processes Vol. 9 (25), no. 3-4 (Proceedings of Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance), 38-49.
  27. Bender, C., Sottinen, T. and Valkeila, E. (2007) Arbitrage with fractional Brownian motion? Theory of Stochastic Processes 13 (29), 23-34.
  28. Sottinen, T. and Viitasaari, L. (2015) Fredholm representation of multi-parameter Gaussian processes with applications to equivalence in law and series expansions. Modern Stochastics: Theory and Applications, 2, No 3 (Proceedings of PRESTO-2015 conference), 287-295.

    Book chapters with referee system

  29. Gasbarra, D., Sottinen, T. and Valkeila, E. (2007) Gaussian bridges. Stochastic Analysis and Applications. Volume 2 of the series Abel Symposia, pp. 361-382.
  30. Bender, C., Sottinen, T. and Valkeila, E. (2011) Fractional procesess as models in stochastic finance. Advanced Mathematical Methods for Finance. Series in Mathematical Finance, Springer, pp.75-103.

    Preprints

  31. Sottinen, T. and Valkeila, E. (2001) Fractional Brownian motion as a model in finance. University of Helsinki, Department of Mathematics, Preprint 302.
  32. Rasila, A. and Sottinen, T. (2015) Yukawa Potential, Panharmonic Measure and Brownian Motion. Preprint, arXiv:1310.2176.
  33. Yang, X., Rasila, A. and Sottinen, T. (2015) Efficient simulation of Schrödinger equation with piecewise constant positive potential. Preprint, arXiv:1512.01306.
  34. Sottinen, T. and Viitasaari, L. (2017) Conditional-Mean Hedging Under Transaction Costs in Gaussian Models. Preprint, arXiv:1708.03242.

    Other mathematical publications

  35. Sottinen, T. (2004) Nobelin muistopalkinto taloustieteestä 2003: R. Englen ARCH-malli. Arkhimedes 2004:2, 10-12 (in Finnish).
  36. Sottinen, T. (2004) Sattuman matematiikkaa III: Kolmogorovin aksioomat ja frekvenssitulkinta. Solmu 2004:2, 17-21 (in Finnish).
  37. Lehto, S. and Sottinen, T. (2005) Sisarusongelma - paradoksi ehdollisesta todennäköisyydestä. Solmu 2005:1, 14-15 (in Finnish).
  38. Rasila, A., and Sottinen, T. (2005) Algebra, PlayStation ja älykkyys. Solmu Erikoisnumero 1/2005-2006 (in Finnish).
  39. Norros, I. and Sottinen, T. (2013) Esko Valkeila 1951-2012. Arkhimedes 2013:1, 30-33 (in Finnish).
  40. Sottinen, T. (2015) BS-kaava ja lama. Arkhimedes 2015:1, 26-30 (in Finnish).

List of publications from AMS Mathematical Reviews, Zentralblatt MATH, and Google Scholar.

Collaborators

  1. Ehsan Azmoodeh, Ruhr University Bochum, Germany
  2. Christian Bender, Saarland University, Germany
  3. Pavel Gapeev, London School of Economics, UK
  4. Dario Gasbarra, University of Helsinki, Finland
  5. Hagen Gilsing
  6. Yuriy Kozachenko, Taras Shevchenko Kyiv National University, Ukraine
  7. Igor Morlanes, Stockholm University, Sweden
  8. Mikko S. Pakkanen, Imperial College London, UK
  9. Antti Rasila, Aalto University, Finland
  10. Simo Särkkä, Aalto University, Finland
  11. Foad Shokrollahi, University of Vaasa, Finland
  12. Ciprian Tudor, University of Lille 1, France
  13. Esko Valkeila
  14. Olga Vasylyk, Taras Shevchenko Kyiv National University, Ukraine
  15. Lauri Viitasaari, Aalto University, Finland
  16. Xuxin Yang, Hunan First Normal University, PRC
  17. Adil Yazigi, University of Vaasa, Finland
  18. Harry van Zanten, University of Amsterdam, The Netherlands

Talks

  1. Fractional Brownian motion, random walks, and binary market models, The 2nd Nordic-Russian Symposium on Stochastic Analysis, Beitostoelen, Norway, 1-6 August 1999.
  2. Fractional Brownian Motion as a Model in Finance, Analysis of High Frequency Data: Annual Meeting of the Finnish Statistical Society, Vaasa, Finland, 17-18 May 2001.
  3. Sample path large deviations of a Gaussian process with stationary increments and regularly varying variance, 12th European Young Statisticians Meeting, Janska Dolina, Slovakia, 4-8 September, 2001.
  4. Busy periods of a fractional Brownian type Gaussian storage, A conference dedicated to the 90th anniversary of B. V. Gnedenko, Kyiv, Ukraine, 3-7 June 2002.
  5. On Gaussian stochastic differential equations with fractional Brownian noise, Laugarvatn Workshop: Stochastic Analysis and its Applications, Laugarvatn, Iceland, 2-7 August 2002.
  6. Arbitrage in the fractional Black-Scholes model, Seminar in Mathematical Statistics, University of Stockholm, Stockholm, Sweden, 16 January, 2003.
  7. Power series series expansions of fractional Brownian motion, The Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance, Laspi, Ukraine, September 2003. (Invited)
  8. Gaussian bridges, Groupe de travail: Processus Stochastiques, Matrices Aléatoires, University of Paris VI, Paris, France, 15 January 2004.
  9. Representations of Gaussian bridges, DYNSTOCH Workshop, Copenhagen, Denmark, 3-5 June 2004.
  10. Fractional Brownian Motions and Sheets, Porkkala Fractional Symposium, Porkkala, Finland, 25 May 2005.
  11. Gaussian Bridges, 35th International Probability Summer School, Saint-Flour, France, 6-23 July 2005.
  12. Replication and Absence of Arbitrage in Non-Semimartingale Models, The Finnish Mathematical Days and the Second Finnish-Estonian Mathematical Colloquium, Tampere, Finland, 4-5 January 2006.
  13. Replication and Absence of Arbitrage in Non-Semimartingale Models, Probability Seminar, University of Barcelona, Barcelona, Spain, 15 March 2006.
  14. Are stylized facts irrelevant in option-pricing? International Conference Modern Stochastics: Theory and Applications, Kyiv, Ukraine, 19-23 June 2006.
  15. On Skorohod-type stochastic differential equations with respect to fractional Brownian motion, 31st Conference on Stochastic Processes and their Applications, Paris, France, 17-21 July 2006. (Invited)
  16. Black-Scholes Prices with Stylized Facts, Russian-Scandinavian Symposium: Probability Theory and Applied Probability, Petrozavodsk, Russia, 26-31 August 2006.
  17. Black-Scholes-hinnoittelumallin robustisuus ja tyylitellyt tosiseikat, Monthly meeting of the Actuarial Society of Finland, 10 October, 2006.
  18. Conditional Small Balls and No-Arbitrage, Advances in Mathematical Finance, Second General AMAMEF Conference and Banach Center Conference, Bedlewo, Poland, 30 April-5 May 2007. (Invited)
  19. What is the Price of the Future?, The Icelandic Centre of Excellence in Theoretical Computer Science ICE-TCS Third Symposium on Theoretical Computer Science, Reykjavik, Iceland, 10 August 2007.
  20. Local Continuity Of Stopping Times And Arbitrage, Workshop and Mid-Term Conference on Advanced Mathematical Methods for Finance, Vienna, Austria, 17-22 September 2007.
  21. Local Continuity, Mathematics Seminar, University of Iceland, Iceland, 25 October 2007.
  22. Probability is irrelevant in stochastic finance: Black-Scholes model is correct despite of stylized facts, Annual meeting of the Icelandic Mathematical Society, Borgarnes, Iceland, 29-30 November 2007. (Invited)
  23. Local Continuity (for Stopping Times), the Finnish Mathematical Days, Espoo, Finland, 3-4 January 2008. (Invited)
  24. Local Continuity, Workshop on Limit theorems and Applications, Paris, France, 14-16 January 2008. (Invited)
  25. What is Volatility?, The 6th NoonToNoon Meeting: Insurance and Financial Mathematics - Theory and Practice, Jyväskylä, Finland, 2-3 October 2008.
  26. Non-semimartingales in finance, 1st Northern Triangular Seminar, Espoo, Finland, 9-11 March 2009. (Tutorial)
  27. On Conditional Full Support with Applications to Mathematical Finance, 25th Nordic and 1st British-Nordic congress of Mathematicians, Oslo, Norway, 8-11 June 2009. (Invited)
  28. Conditional full support for Gaussian processes with stationary increments, Modern Stochastics: Theory and Applications II, Kyiv, Ukraine, 7-11 September, 2010. (Invited)
  29. "Todellinen" veroprosentti: Kaksi ajankohtaista esimerkkiä talousmatematiikasta ja "todellisuudesta", MAOL ry:n syyspäivät, Vantaa, Finland, 8-10 October, 2010. (Invited)
  30. Pricing by hedging and no-arbitrage beyond semimartingales, International symposium: Visions in stochastics (Leaders and their Pupils), Moscow, Russia, 1-3 November, 2010.
  31. No-Arbitrage with Non-Semimartingales: Continuous Simple Arbitrage Case, Seventh Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Switzerland, 23-27 May, 2011.
  32. Black ja Scholes ilman Gaussia, Annual meeting of the Finnish Mathematical Society, Helsinki, Finland, 19 March, 2012. (Invited)
  33. Generalized Gaussian Bridges of Prediction-Invertible Processes, Presentation at Hunan Normal University, Changsha, China, 22 May, 2012.
  34. Black-Scholes Prices and Hedges for Financial Derivatives in Non-Gaussian Non-Martingale Models, International Conference on Applied Mathematics 2012, Modeling, Analysis & Computation, City University of Hong Kong, Hong Kong, China, 30 May, 2012.
  35. Yukawa Potential, Harmonic Measure and Killing Brownian Motion, First Chinese-Finnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications, Turku, Finland, 18 August, 2012.
  36. Generalized Gaussian Bridges of Prediction-Invertible Processes, Modern Stochastics: Theory and Applications III, Kyiv, Ukraine, 10 September, 2012. (Invited)
  37. Generalized Gaussian Bridges, Marrakesh International Conference on Probability and Statistics, Marrakesh, Morocco, 19 December, 2013. (Plenary)
  38. Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, Thiele Seminar, Aarhus University, Århus, Denmark, 26 March, 2014.
  39. Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, ICM 2014, Seoul, Republic of Korea, 19 August, 2014.
  40. Representing Gaussian Processes with Martingales with Application to MLE of Langevin Equation, Stochastic Visit Workshop of the FDPSS, Tartu, Estonia, 12 September, 2014.
  41. Gaussian Fredholm Processes, International Conference: Probability, Reliability and Stochastic Optimization, Kyiv, Ukraine, 8 April, 2015. (Plenary)
  42. Matematiikan täsmäopetuksella parempia insinöörejä, Interaktiivinen tekniikka koulutuksessa, ITK2015, Hämeenlinna, 17 April, 2015.
  43. Gaussian Fredholm Processes with Applications, Yu.V.Linnik Centennial Conference, Euler International Mathematical Institute, St. Petersburg, Russia, 16 September, 2015.
  44. Representing Gaussian Processes via Brownian Motion with Applications to Stochastic Analysis, talk at South Central University, Changsha, PRC, 30 October, 2015.
  45. A Celebration of Dynkin's Formula, tutorial at Hunan First Normal University, Changsha, PRC, 26 November, 2015.
  46. Walk On Spheres Algorithms for Helmholtz and Linearized Poisson-Boltzmann Equations, The Fifth Chinese-Finnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications, Aalto University, Espoo, Finland, 9 February, 2016.
  47. Parameter Estimation for the Langevin Equation with Stationary-Increment Gaussian Noise, Lorentz Center Workshop Fractatility and Fractionality, University of Leiden, Leiden, The Netherlands, 19 May, 2016. (Invited)
  48. Gaussian (Fredholm) Processes, 37th Finnish Summer School on Stochastics and Statistics, Lammi, Finland, 30 May, 2016.
  49. Hedging under transaction costs in Gaussian models, Barcelona Workshop on Mathematical Finance, Barcelona, Spain, 29 March, 2017.

Other activities

  • Organized the international conference Fractional Brownian days together with Esko Valkeila.
  • Member of the organizing committee of the international symposium SF-180: Snapshots of Stochastics Frontiers at 180 Degrees: Symposium celebrating the 60th birthdays of Esa Nummelin, Paavo Salminen, and Esko Valkeila.
  • Member of the organizing committee of the 34th-36th Finnish Summer School on Probability Theory and Statistics.
  • Referee for the journals Aerospace Science and Technology, Advances in Applied Probability, Afrika Matematika, Annales Mathématiques Blaise Pascal, Annals of Applied Probability, Annals of Finance, Annals of the Institute of Statistical Mathematics, Bernoulli (4), Brazilian Journal of Probability and Statistics, Communications on Stochastic Analysis, Computers and Mathematics with Applications, Decisions in Economics and Finance, Electronic Communications in Probability (3), Electronic Journal of Probability (2), Extremes, Finance and Stochastics, IEEE Transactions on Information Theory, IMA Journal of Management Mathematics, International Journal of Theoretical and Applied Finance (6), Journal of Applied Mathematics and Computing, Journal of Applied Probability, Journal of Computational and Applied Mathematics, Journal of Economics, Journal of Integral Equations and Applications, Journal of Probability and Statistics, Journal of Theoretical Probability (2), Lithuanian Mathematical Journal, Mathematics and Financial Economics (2), Methodology and Computing in Applied Probability, Modern Stochastics: Theory and Applications, OPSEARCH: Journal of the operational research society of India, Physica A: Statistical Mechanics and its Applications (3), Quantitative Finance, Queueing Systems (2), Statistics: A Journal of Theoretical and Applied Statistics, Statistics and Probability Letters (4), Statistics, Optimization & Information Computing , Stochastic Analysis and Applications (5), Stochastic and Dynamics (3), Stochastics and Stochastics Reports , Stochastics: An International Journal Of Probability And Stochastic Processes , Stochastic Processes and their Applications (9), World Scientific Publishing Co. (book proposal, 2)
  • Reviewer for Nederlandse Organisatie voor Wetenschappelijk Onderzoek 2008 and 2010, for Fonds zur Förderung der wissenschaftlichen Forschung 2013, for Fundação para Ciência e a Tecnologia 2012 and 2013, and for Narodowe Centrum Nauki 2015.
  • Member of evaluation panel for Fundação para Ciência e a Tecnologia 2015, 2017.
  • Reviewer for the AMS Mathematical Reviews, 2003-2014.
  • Reviewer for Zentrablatt MATH, 2011-2015.

Ph.D. students

  1. Ph.D. Mikko S. Pakkanen (University of Helsinki, 2010)
  2. Ph.D. Lauri Viitasaari (Aalto University, 2014)
  3. Ph.D. Adil Yazigi (University of Vaasa, 2015)
  4. Mr. Foad Shokrollahi
  5. Ms. Josephine Dufitinema