University of Vaasa Department of Mathematics and Statistics
Faculty of Technology
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Research

Research interests

Fractional, Gaussian, self-similar, and quadratic variation processes; stochastic analysis; statistics for stochastic processes; simulation of stochastic processes; 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. (2001) Avtomodel'ni protsesy zy statsyunarnymy pryrostamy z prostoriv SSub_\phi(\Omega). Teoriya Imovirnostei ta Matematichna Statistika 65, 67-78 (in Ukrainian).
    Self-similar processes with stationary increments in the spaces SSub_\phi(\Omega). Theory of Probability and Mathematical Statistics 65, 77-88 (English translation).
  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 & Decisions 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. (2010) Lipschitz conditions for Sub_\phi(\Omega)-processes with application to weakly self-similar stationary increment processes. Teor. Imovir. ta Matem. Statyst. 82, 67-81.
  14. Gapeev, P., Sottinen, T. and Valkeila, E. (2011) Robust replication in H-self-similar Gaussian market models under uncertainty. Statistics & Decisions 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.

    Proceedings with referee system

  16. 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.
  17. Bender, C., Sottinen, T. and Valkeila, E. (2007) Arbitrage with fractional Brownian motion? Theory of Stochastic Processes 13(29), 23-34.

    Book chapters with referee system

  18. Gasbarra, D., Sottinen, T. and Valkeila, E. (2007) Gaussian bridges. Stochastic Analysis and Applications: The Abel Symposium 2005. (Eds. F. Benth, G. Di Nunno, T. Lindstrøm, B. Øksendal and T. Zhang) Abel Symposia, Springer.
  19. Bender, C., Sottinen, T. and Valkeila, E. (2011) Fractional procesess as models in stochastic finance. Advanced Mathematical Methods for Finance (Eds. G. Di Nunno and B. Øksendal) Series in Mathematical Finance, Springer.

    Preprints

  20. Sottinen, T. and Valkeila, E. (2001) Fractional Brownian motion as a model in finance. University of Helsinki, Department of Mathematics, Preprint 302.

    Other mathematical publications

  21. Sottinen, T. (2004) Nobelin muistopalkinto taloustieteestä 2003: R. Englen ARCH-malli. Arkhimedes 2004:2, 10-12 (in Finnish).
  22. Sottinen, T. (2004) Sattuman matematiikkaa III: Kolmogorovin aksioomat ja frekvenssitulkinta. Solmu 2004:2, 17-21 (in Finnish).
  23. Lehto, S. and Sottinen, T. (2005) Sisarusongelma - paradoksi ehdollisesta todennäköisyydestä. Solmu 2005:1, 14-15 (in Finnish).
  24. Rasila, A., and Sottinen, T. (2005) Algebra, PlayStation ja älykkyys. Solmu Erikoisnumero 1/2005-2006 (in Finnish).

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

Collaborators

  1. Christian Bender, Saarland University
  2. Pavel Gapeev, London School of Economics
  3. Dario Gasbarra, University of Jyväskylä
  4. Hagen Gilsing, Humboldt University in Berlin
  5. Yuriy Kozachenko, Taras Shevchenko Kyiv National University
  6. Igor Morlanes, Aalto University
  7. Antti Rasila, Aalto University
  8. Simo Särkkä, Aalto University
  9. Ciprian Tudor, University of Lille 1
  10. Esko Valkeila, Aalto University
  11. Olga Vasylyk, Taras Shevchenko Kyiv National University
  12. Harry van Zanten, Eindhoven University of Technology

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.

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
  • Referee for the journals
    1. Aerospace Science and Technology
    2. Advances in Applied Probability
    3. Afrika Matematika
    4. Annales Mathématiques Blaise Pascal
    5. Annals of Applied Probability
    6. Annals of Finance
    7. Brazilian Journal of Probability and Statistics
    8. Communications on Stochastic Analysis
    9. Computers and Mathematics with Applications
    10. Decisions in Economics and Finance
    11. Electronic Communications in Probability
    12. Electronic Journal of Probability
    13. Extremes
    14. IMA Journal of Management Mathematics
    15. International Journal of Theoretical and Applied Finance (2)
    16. Journal of Applied Mathematics and Computing
    17. Journal of Applied Probability
    18. Journal of Economics
    19. Journal of Probability and Statistics
    20. Quantitative Finance
    21. Statistics, A Journal of Theoretical and Applied Statistics
    22. Statistics and Probability Letters
    23. Stochastic Analysis and Applications (3)
    24. Stochastics and Stochastics Reports
    25. Stochastic Processes and Applications (6)
    26. World Scientific Publishing Co. (book proposal, 2)
  • Reviewer for NWO Veni Scheme 2010.
  • Reviewer for NWO Free Competition 2008 EW.
  • Reviewer for the AMS Mathematical Reviews, 2003- (18 reviews).

Past and present Ph.D. students

  1. Ph.D. Mikko S. Pakkanen (2010)
  2. M.Sc. Adil Yazigi
  3. M.Sc. Matti Rantanen