Stochastics
Stochastic analysis and modeling are key methodologies for analyzing random interactions in today's financial and information systems. The stochastics research group applies and develops methods in stochastic analysis, optimization, martingale theory, Markov processes, and mathematical statistics. The main research themes are limits of random processes, coupling techniques, and numerical stochastic methods. The main applications are in mathematical finance, risk management, information networks, and statistics.
People
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Professor Esko Valkeila |
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Research fellow Lasse Leskelä |
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PhD student Ari-Pekka Perkkiö |
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Lecturer Ilkka Mellin |
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PhD student Helena Aro |
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PhD student Heikki Tikanmäki |
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Docent Teemu Pennanen |
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PhD student Ehsan Azmoodeh |
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Research assistant Lotte van den Berg |
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Docent Karl Sigman |
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PhD student Igor Morlanes |
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Research assistant Lauri Viitasaari |
Part-time PhD students: Matias Leppisaari, Mika Sirviö.
Projects
- Approximation, Comparison, and Optimization of Stochastic Processes, 2009-2012.
- Stability and Control of Stochastic Processing Networks, 2008-2010.
- More...
Publications
Publications of the group can be found on the arXiv preprint server and MathSciNet database. The most up-to-date information is available on the members' personal web pages.
Selected articles
- L. Leskelä. Stochastic relations of random variables and processes. Journal of Theoretical Probability, to appear.
- T. Pennanen. Arbitrage and martingales in illiquid markets. Finance and Stochastics, to appear.
- T. Pennanen. Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Mathematical Programming 116:461-479, 2009.
- C. Bender, T. Sottinen, E. Valkeila. Pricing by hedging and no-arbitrage beyond semimartingales. Finance and Stochastics 12(4):441-468, 2008.
- K. Dzhaparidze, P. Spreij, E. Valkeila. Information processes for semimartingale experiments. Annals of Probability 31(1):216-243, 2003.
Teaching
The group members teach undergraduate and advanced courses in probability and statistics. The undergraduate courses are usually given in Finnish. The offered stochastics courses are eligible as a basis for an SHV degree in insurance mathematics.
Collaboration
The group has numerous international and domestic research contacts. The group is affiliated with the following international research networks:
- AMaMeF - Advanced Mathematical Methods for Finance
- DYNSTOCH - Statistical Methods for Dynamical Stochastic Models