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T.1. Financial Mathematics

Theme leader: P.J.C. Spreij

Description of the theme.
Financial Mathematics is a relatively new branch in applied mathematics. Recent years have seen a truly quantitative revolution in the world of finance. The call for advanced mathematical techniques has boosted research in new directions of applied mathematics, both of a theoretical and a practical nature. Many researchers from more traditional branches of mathematics have made major contributions.
Within the Netherlands only a few mathematicians devote a major part of their research to this field. The newly installed Stieltjes theme group on Financial Mathematics is a new initiative to coordinate research in The Netherlands and to be a platform on which various activities in this field find a common base.
Activities of the theme group are by no means restricted to participants of the Stieltjes Institute itself. This is reflected by the composition of the steering committee and of the theme group as a whole, where also mathematicians from other research institutes have been included.
The theme group has strong connections with several research programmes of the Stieltjes Institute, in particular with Probability, Statistics, Operator theory and Evolutionary Systems, and equally well established links with other research institutes in the Netherlands like CentER, DISC, EURANDOM and MRI.

Status of the theme.
The members of the theme group have been active in various fields like probability theory, mathematical statistics, time series analysis and dynamical systems.
It is the ambition of the theme group to promote the research in Financial Mathematics in the Netherlands by organising a seminar series, workshops and special activities in the educational vein. All these activities will be conducted in close cooperation with members of the mathematical institutes associated with the Stieltjes Institute and with other research institutes both in mathematics and in economics. The theme group started its activities in mid 2000.

The main activities, apart form research, aimed at promoting Financial Mathematics have been the organisation of a Stieltjes Onderwijsweek on Financial Mathematics, a Winter School on Mathematical Finance and a session on Financial Mathematics at the Dutch Mathematical Congress 2001.

A more detailed description of these activities follows.
- The Stieltjes Onderwijsweek on Financial Mathematics has been held at the Lorentz Centre (Leiden) from March 5-9, 2001. This week has been organised by Svetlana Borovkova (TUD) and Peter Spreij (UvA) and the courses were given by Svetlana Borovkova (TUD), Bernard Hanzon (VU), Andreas Kyprianou (UU) and Michel Vellekoop (UT). Special invited lectures on Applications of Financial Mathematics in practice have been delivered by Dietmar Salome (Rabobank Derivatives) and Peter van Driel (Shell). There were nine participating students from many different universities in The Netherlands.
- The Winter School on Mathematical Finance has been held at the Conference centre Oud-Poelgeest (Oegstgeest) from December 17-19, 2001.
This Winter School has been organised by Hans Schumacher (KUB) and Peter Spreij (UvA). Minicourses have been given by David Heath (Carnegie Mellon) on Risk measures and by Tomas Björk (Stockholm School of Economics) on Interest rate theory. Special invited lectures have been given by Chris Rogers (Bath), Stewart Hodges (Warwick) and Antoon Pelsser (EUR, Nationale Nederlanden). There were also six short lectures by researchers on Financial Mathematics form The Netherlands. Over fifty particpants have attended the Winter School. Because of the enthousiastic reactions of the participants a follow up in December 2002 has already been planned. The Winter School has been sponsored by the Stieltjes Institute, MRI, CentER and NWO.
- The theme group was also involved in the organisation of a Special Session on Financial Mathematics at the Dutch Mathematical Congress held at the Vrije Universiteit on April 19-20, 2001. The speakers were Antoon Pelsser (EUR, Nationale Nederlanden), Jeroen Kerkhof (KUB), Andre de Vries (ABN AMRO) and Suresh Kumar (UT).

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