Bernard Hanzon

Bernand Hanzon is an academic, mathematician, and researcher. He has worked on systems theory, probability and statistics, and mathematical finance. He is best known for a number of results in these areas.

Nonlinear filtering: Projection filters

Hanzon introduced the idea of Projection Filter in Hanzon (1987) and Hanzon and Hut (1991), then fully developed and formalized with the help of Damiano Brigo and Francois Le Gland. The Projection filters are a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry. This has been a contribution to approximate solutions to the filtering problem (stochastic processes), that has been applied to optics by van Handel and Mabuchi (2005). It has also been considered by the Swedish Defense Research Agency in Berefelt, Hamberg and Robinson (2003), and cited in the context of GPS and navigation in connection with the use of the exponential family for the approximated nonlinear filter in Azimi-Sadjadi and Krishnaprasad (2005). Hanzon, with Brigo, has also explored the possible use of Filtering techniques in Mathematical Finance (1998).

Current and past affiliations

Hanzon is currently Associate Professor of Mathematical Finance at the University College Cork, College of Science, Engineering and Food Science, School of Mathematical Sciences, Cork, Ireland. His current interests include mathematical finance and algebraic methods in systems theory. Prior to that Hanzon had been an assistant professor at the Free University of Amsterdam. Hanzon holds a PhD in Systems Theory.

Notable students

The Mathematics genealogy project lists Damiano Brigo as a PhD student of Hanzon and Jan van Schuppen.

References

  • Bernard Hanzon. A differential-geometric approach to approximate nonlinear filtering. In C.T.J. Dodson, Geornetrization of Statistical Theory, pages219–223,ULMD Publications, University of Lancaster, 1987.
  • Hanzon, B. and Hut, R. (1991) New results on the projection filter. Proceedings of the First European Control Conference, Grenoble, 1991, Vol. I
  • Azimi-Sadjadi, B.; Krishnaprasad, P.S. Approximate nonlinear filtering and its applications for GPS. Decision and Control, 2000. Proceedings of the 39th IEEE Conference on, Volume 2, Issue , 2000 Page(s):1579 - 1584 vol.2. Digital Object Identifier 10.1109/CDC.2000.912085
  • Azimi-Sadjadi, B.; Krishnaprasad, P.S. Approximate nonlinear filtering and its applications in Navigation. Automatica, Volume 41, Issue 6, June 2005, Pages 945-956
  • Berefelt,F., Hamberg,J., and Robinson, J. W. C. (2003). Geometric Aspects of Nonlinear Filtering. FOI-R--1074--SE, 1650--1942, Scientific Report, available here
  • Brigo, D, Hanzon, B, On some filtering problems arising in mathematical finance, Insurance: Mathematics and Economics, 1998, Vol: 22, Pages: 53 - 64
  • Brigo, D, Hanzon, B, LeGland, F, A differential geometric approach to nonlinear filtering: The projection filter, IEEE T AUTOMAT CONTR, 1998, Vol: 43, Pages: 247 - 252, ISSN: 0018-9286
  • Brigo, D, Hanzon, B, Le Gland, F, Approximate nonlinear filtering by projection on exponential manifolds of densities, BERNOULLI, 1999, Vol: 5, Pages: 495 - 534, ISSN: 1350-7265
  • Ramon van Handel and Hideo Mabuchi, Quantum projection filter for a highly nonlinear model in cavity QED, 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S226-S236
  • Christiaan Heij (Editor), Hans Schumacher (Editor), Bernard Hanzon (Editor), Kees Praagman (Editor). System Dynamics in Economic and Financial Models (Financial Economics & Quantitative Analysis), Wiley, 1997
  • Bernard Hanzon and Michiel Hazewinkel (eds.) . Constructive Algebra and Systems Theory, 2006, vi + 358 pp, ISBN 90-6984-477-X