
Research
Research interests
Fractional, Gaussian, selfsimilar, and quadratic variation processes;
stochastic analysis; statistics for stochastic processes; stochastic simulation;
mathematical finance; financial engineering.
Publications
Refereed publications
 Sottinen, T. (2001)
Fractional Brownian motion, random walks and binary market models.
Finance and Stochastics 5, no. 3, 343355.
 Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2002)
Selfsimilar processes with stationary increments
in the spaces SSub_\phi(\Omega).
Theory of Probability and Mathematical Statistics 65, 7788 .
 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, 113129.
 Sottinen, T. and Valkeila, E. (2003)
On arbitrage and replication in the Fractional BlackScholes pricing model.
Statistics & Risk Modeling 21, 93107.
 Gilsing, H. and Sottinen, T. (2003)
Power series expansions for fractional Brownian motions.
Theory of Stochastic Processes Vol. 9 (25), no. 34 (Proceedings of Seventh International School on Mathematical and Statistical Methods in Economics, Finance and Insurance), 3849.
 Sottinen, T. (2003)
Fractional Brownian motion in finance and queueing.
Ph.D. Thesis, University of Helsinki.
 Sottinen, T. (2004)
On Gaussian processes equivalent in law to fractional Brownian motion.
Journal of Theoretical Probability 17, no. 2, 309325.
 Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2005)
Simulation
of weakly selfsimilar stationary increment Sub_\phi(\Omega)processes: a series expansion approach.
Methodology and Computing in Applied Probability 7, 379400.
 Sottinen, T. and Tudor, C.A. (2006)
On the equivalence of multiparameter Gaussian processes.
Journal of Theoretical Probability 19, no. 2., 461485.
 Gasbarra, D., Sottinen, T. and Valkeila, E. (2007)
Gaussian
bridges.
Stochastic Analysis and Applications. Volume 2 of the series Abel Symposia, pp. 361382.
 Bender, C., Sottinen, T. and Valkeila, E. (2007)
Arbitrage with fractional Brownian motion?
Theory of Stochastic Processes 13 (29), 2334.
 Sottinen, T. and Tudor, C.A. (2008)
Parameter
estimation for stochastic equations with additive fractional Brownian sheet.
Statistical Inference for Stochastic Processes 11, 221236.
 Särkkä, S. and Sottinen, T. (2008)
Application of Girsanov Theorem to Particle Filtering of Discretely Observed ContinuousTime NonLinear Systems.
Bayesian Analysis 3, no. 3., 555584.
 Bender, C., Sottinen, T. and Valkeila, E. (2008)
Pricing by hedging and noarbitrage beyond semimartingales.
Finance and Stochastics 12, 441468.
 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, 223233.
 Kozachenko, Yu., Sottinen, T. and Vasylyk, O. (2011)
Lipschitz conditions for
Sub_\phi(\Omega)processes with application to weakly selfsimilar stationary increment processes.
Theory Probab. Math. Stat. 82, 5773.
 Gapeev, P., Sottinen, T. and Valkeila, E. (2011)
Robust replication in Hselfsimilar Gaussian market models under uncertainty.
Statistics & Risk Modeling 28, 3750.
 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., 561568.
 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.75103.
 Sottinen, T. and Yazigi, A. (2014)
Generalized Gaussian Bridges.
Stochastic Processes and their Applications 124, Issue 9, 30843105.
 Azmoodeh, E., Sottinen, T., Viitasaari, L. and Yazigi, A. (2014)
Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes.
Statistics & Probability Letters 94, 230235.
 Azmoodeh, E., Sottinen, T. and Viitasaari, L. (2015)
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownianfractional Brownian model.
Modern Stochastics: Theory and Applications, 2, No. 1, 2949.
 Sottinen, T. and Viitasaari, L. (2015)
Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions.
Modern Stochastics: Theory and Applications, 2, No 3 (Proceedings of PRESTO2015 conference), 287295.
 Sottinen, T. and Viitasaari, L. (2016)
Pathwise integrals and ItoTanaka Formula for Gaussian processes.
Journal of Theoretical Probability 29, Issue 2, 590616.
 Sottinen, T. and Viitasaari, L. (2016)
Stochastic Analysis of Gaussian Processes via Fredholm Representation.
International Journal of Stochastic Analysis, doi:10.1155/2016/8694365.
 Pakkanen, M.S., Sottinen, T. and Yazigi, A. (2017)
On the conditional small ball property of multivariate Levydriven moving average processes,
Stochastic Processes and their Applications, 127, Issue 3, 749782.
 Sottinen, T. and Viitasaari, L. (2017)
Parameter Estimation for the Langevin Equation with StationaryIncrement Gaussian Noise.
Statistical Inference for Stochastic Processes, doi:10.1007/s1120301791566.
 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, 589602.
 Sottinen, T. and Viitasaari, L. (2017)
Prediction Law of Fractional Brownian Motion.
Statistics & Probability Letters 129, 155166.
 Shokrollahi, F. and Sottinen, T. (2017)
Hedging in fractional BlackScholes model with transaction costs.
Statistics & Probability Letters 130, 8591.
 Sottinen, T. and Viitasaari, L. (2018)
ConditionalMean Hedging Under Transaction Costs in Gaussian Models.
International Journal of Theoretical and Applied Finance 21, no. 2.
 Rasila, A. and Sottinen, T. (2018)
Yukawa Potential, Panharmonic Measure and Brownian Motion.
Axioms 2018, 7(2), 28.
 Sottinen, T. and Viitasaari, L. (2018)
Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law.
Theory of Probability and Mathematical Statistics 98, to appear.
Preprints
 Sottinen, T. and Valkeila, E. (2001)
Fractional Brownian motion as a model in finance.
University of Helsinki, Department of Mathematics, Preprint 302.
 Yang, X., Rasila, A. and Sottinen, T. (2015)
Efficient simulation of Schrödinger equation with piecewise constant positive potential.
Preprint, arXiv:1512.01306.
Other mathematical publications (in Finnish)
 Sottinen, T. (2004)
Nobelin muistopalkinto
taloustieteestä 2003: R. Englen ARCHmalli.
Arkhimedes
2004:2, 1012
(in Finnish).
 Sottinen, T. (2004)
Sattuman matematiikkaa III:
Kolmogorovin aksioomat ja frekvenssitulkinta.
Solmu 2004:2, 1721
(in Finnish).
 Lehto, S. and Sottinen, T. (2005)
Sisarusongelma  paradoksi
ehdollisesta todennäköisyydestä.
Solmu 2005:1, 1415 (in Finnish).
 Rasila, A., and Sottinen, T. (2005)
Algebra, PlayStation ja
älykkyys.
Solmu
Erikoisnumero 1/20052006 (in Finnish).
 Norros, I. and Sottinen, T. (2013)
Esko Valkeila 19512012.
Arkhimedes
2013:1, 3033 (in Finnish).
 Sottinen, T. (2015)
BSkaava ja lama.
Arkhimedes
2015:1, 2630 (in Finnish).
Lecture notes (some in Finnish)

Rahoitusteoria: Eli
optioiden hinnoittelun ja toistamisen taito tai oppi optioiden
oikeasta hinnasta.,
149 pages, 2006.

Todennäköisyysteoria: Teoria
mitasta, mitallisuudesta, mitattomuudesta ja riippumattomuudesta.,
130 pages, 2006.

Malliavinlaskenta: Eli
gaussisten prosessien derivointi.,
87 pages, 2006.

Operations Research with GNU Linear
Programming Kit,
200 pages, 2009.

Päätöksenteko
epävarmuuden vallitessa,
100 pages, 2009.

Operations Research with GNU Octave,
187 pages, 2010.

Päätöksiä ja Paatoksia,
146 pages, 2011.

Probability and Stochastic Processes with a Twist of GNU Octave towards Queuing, 181 pages, 2018.
Blog rants (in Finnish)
See here.
List of publications from
AMS Mathematical Reviews,
Zentralblatt MATH, and
Google Scholar.
Collaborators
 Ehsan Azmoodeh, Ruhr University Bochum, Germany
 Christian Bender, Saarland University, Germany
 Pavel Gapeev, London School of Economics, UK
 Dario Gasbarra, University of Helsinki, Finland
 Hagen Gilsing
 Yuriy Kozachenko, Taras Shevchenko Kyiv National University, Ukraine
 Igor Morlanes, Stockholm University, Sweden
 Mikko S. Pakkanen, Imperial College London, UK
 Antti Rasila, Aalto University, Finland
 Simo Särkkä, Aalto University, Finland
 Foad Shokrollahi, University of Vaasa, Finland
 Ciprian Tudor, University of Lille 1, France
 Esko Valkeila
 Olga Vasylyk, Taras Shevchenko Kyiv National University, Ukraine
 Lauri Viitasaari, Aalto University, Finland
 Xuxin Yang, Hunan First Normal University, PRC
 Adil Yazigi, University of Vaasa, Finland
 Harry van Zanten, University of Amsterdam, The Netherlands
Talks
 Fractional Brownian motion, random walks, and binary market models,
The 2nd NordicRussian Symposium on Stochastic Analysis, Beitostoelen, Norway, 16 August 1999.
 Fractional Brownian Motion as a Model in Finance,
Analysis of High Frequency Data: Annual Meeting of the Finnish Statistical Society,
Vaasa, Finland, 1718 May 2001.
 Sample path large deviations of a Gaussian process with
stationary increments and regularly varying variance,
12th European Young Statisticians Meeting, Janska Dolina, Slovakia, 48 September, 2001.
 Busy periods of a fractional Brownian type Gaussian storage,
A conference dedicated to the 90th anniversary of B. V. Gnedenko,
Kyiv, Ukraine, 37 June 2002.
 On Gaussian stochastic differential equations with fractional Brownian noise,
Laugarvatn Workshop: Stochastic Analysis and its Applications,
Laugarvatn, Iceland, 27 August 2002.
 Arbitrage in the fractional BlackScholes model,
Seminar in Mathematical Statistics, University of Stockholm, Stockholm, Sweden, 16 January, 2003.
 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)
 Gaussian bridges,
Groupe de travail: Processus Stochastiques, Matrices Aléatoires,
University of Paris VI, Paris, France, 15 January 2004.
 Representations of Gaussian bridges,
DYNSTOCH Workshop, Copenhagen, Denmark, 35 June 2004.
 Fractional Brownian Motions and Sheets,
Porkkala Fractional Symposium, Porkkala, Finland, 25 May 2005.
 Gaussian Bridges, 35th International Probability Summer School,
SaintFlour, France, 623 July 2005.
 Replication and Absence of Arbitrage in NonSemimartingale Models,
The Finnish Mathematical Days and the Second FinnishEstonian Mathematical Colloquium,
Tampere, Finland, 45 January 2006.
 Replication and Absence of Arbitrage in NonSemimartingale Models,
Probability Seminar, University of Barcelona,
Barcelona, Spain, 15 March 2006.
 Are stylized facts irrelevant in optionpricing?
International Conference Modern Stochastics: Theory and Applications,
Kyiv, Ukraine, 1923 June 2006.
 On Skorohodtype stochastic differential equations with respect to
fractional Brownian motion, 31st Conference on Stochastic Processes and their Applications,
Paris, France, 1721 July 2006. (Invited)
 BlackScholes Prices with Stylized Facts,
RussianScandinavian Symposium: Probability Theory and Applied Probability,
Petrozavodsk, Russia, 2631 August 2006.
 BlackScholeshinnoittelumallin robustisuus ja tyylitellyt tosiseikat,
Monthly meeting of the Actuarial Society of Finland, 10 October, 2006.
 Conditional Small Balls and NoArbitrage,
Advances in Mathematical Finance, Second General AMAMEF Conference and Banach Center Conference,
Bedlewo, Poland, 30 April5 May 2007. (Invited)
 What is the Price of the Future?,
The Icelandic Centre of Excellence in Theoretical Computer Science ICETCS
Third Symposium on Theoretical Computer Science, Reykjavik, Iceland, 10 August 2007.
 Local Continuity Of Stopping Times And Arbitrage, Workshop and MidTerm Conference on Advanced Mathematical Methods for Finance, Vienna, Austria, 1722 September 2007.
 Local Continuity,
Mathematics Seminar, University of Iceland, Iceland, 25 October 2007.
 Probability is irrelevant in stochastic finance:
BlackScholes model is correct despite of stylized facts, Annual meeting of the Icelandic Mathematical Society,
Borgarnes, Iceland, 2930 November 2007. (Invited)
 Local Continuity (for Stopping Times), the Finnish Mathematical Days,
Espoo, Finland, 34 January 2008. (Invited)
 Local Continuity, Workshop on Limit theorems and Applications,
Paris, France, 1416 January 2008. (Invited)
 What is Volatility?,
The 6th NoonToNoon Meeting:
Insurance and Financial Mathematics  Theory and Practice,
Jyväskylä, Finland,
23 October 2008.
 Nonsemimartingales in finance,
1st Northern Triangular Seminar, Espoo, Finland,
911 March 2009. (Tutorial)
 On Conditional Full Support with Applications to Mathematical Finance,
25th Nordic and 1st BritishNordic congress of Mathematicians, Oslo, Norway, 811 June 2009. (Invited)
 Conditional full support for Gaussian processes with stationary increments,
Modern Stochastics: Theory and Applications II, Kyiv, Ukraine, 711 September, 2010. (Invited)
 "Todellinen" veroprosentti:
Kaksi ajankohtaista esimerkkiä talousmatematiikasta ja "todellisuudesta",
MAOL ry:n syyspäivät, Vantaa, Finland, 810 October, 2010. (Invited)
 Pricing by hedging and noarbitrage beyond
semimartingales,
International symposium: Visions in stochastics (Leaders and their Pupils), Moscow, Russia, 13 November, 2010.
 NoArbitrage with
NonSemimartingales: Continuous Simple Arbitrage Case,
Seventh Seminar on Stochastic Analysis, Random Fields and
Applications, Ascona, Switzerland, 2327 May, 2011.
 Black
ja Scholes ilman Gaussia,
Annual meeting of the Finnish Mathematical Society, Helsinki, Finland,
19 March, 2012. (Invited)
 Generalized Gaussian Bridges of PredictionInvertible Processes,
Presentation at Hunan Normal University, Changsha, China,
22 May, 2012.
 BlackScholes Prices and Hedges for Financial Derivatives in NonGaussian NonMartingale Models,
International Conference on Applied Mathematics 2012,
Modeling, Analysis & Computation,
City University of Hong Kong,
Hong Kong, China,
30 May, 2012.
 Yukawa Potential, Harmonic Measure and Killing Brownian Motion,
First ChineseFinnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications,
Turku, Finland,
18 August, 2012.
 Generalized Gaussian Bridges of PredictionInvertible Processes,
Modern Stochastics: Theory and Applications III,
Kyiv, Ukraine,
10 September, 2012. (Invited)
 Generalized Gaussian Bridges,
Marrakesh International Conference on Probability and Statistics,
Marrakesh, Morocco,
19 December, 2013. (Plenary)
 Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, Thiele Seminar, Aarhus University, Århus, Denmark, 26 March, 2014.
 Necessary and Sufficient Conditions for Hölder Continuity of Gaussian Processes, ICM 2014, Seoul, Republic of Korea, 19 August, 2014.
 Representing Gaussian Processes with Martingales with Application to MLE of Langevin Equation, Stochastic Visit Workshop of the FDPSS, Tartu, Estonia, 12 September, 2014.
 Gaussian Fredholm Processes, International Conference: Probability, Reliability and Stochastic Optimization, Kyiv, Ukraine, 8 April, 2015. (Plenary)
 Matematiikan täsmäopetuksella parempia insinöörejä, Interaktiivinen tekniikka koulutuksessa, ITK2015, Hämeenlinna, 17 April, 2015.

Gaussian Fredholm Processes with Applications, Yu.V.Linnik Centennial Conference, Euler International Mathematical Institute, St. Petersburg, Russia, 16 September, 2015.
 Representing Gaussian Processes via Brownian Motion with Applications to Stochastic Analysis, talk at South Central University, Changsha, PRC, 30 October, 2015.
 A Celebration of Dynkin's Formula, tutorial at Hunan First Normal University, Changsha, PRC, 26 November, 2015.
 Walk On Spheres Algorithms for Helmholtz and Linearized PoissonBoltzmann Equations, The Fifth ChineseFinnish Seminar and Workshop on Modern Trends in Classical Analysis and Applications, Aalto University, Espoo, Finland, 9 February, 2016.
 Parameter Estimation for the Langevin Equation with StationaryIncrement Gaussian Noise, Lorentz Center Workshop Fractatility and Fractionality, University of Leiden, Leiden, The Netherlands, 19 May, 2016. (Invited)
 Gaussian (Fredholm) Processes, 37th Finnish Summer School on Stochastics and Statistics, Lammi, Finland, 30 May, 2016.
 Hedging under transaction costs in Gaussian models, Barcelona Workshop on Mathematical Finance, Barcelona, Spain, 29 March, 2017.
Ph.D. students
 Dr. Mikko S. Pakkanen (University of Helsinki, 2010)
 Dr. Lauri Viitasaari (Aalto University, 2014)
 Dr. Adil Yazigi (University of Vaasa, 2015)
 Dr. Foad Shokrollahi (University of Vaasa)
 Ms. Josephine Dufitinema (University of Vaasa)
