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University of Hamburg - Department of Mathematics
Center of Mathematical Statistics and Stochastic Processes
Hamburger Zentrum für Versicherungswissenschaft (HZV)


Informations:

From 1 September 2007:

I am Lecturer in Applied Mathematics at the Department of Mathematics at University of Leicester.
My new postal address is:

Dr. Bero Roos
Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

E-mail:new email roos

Tel.: +44 (0) 116 252 3889

My new home page

Summer 2006:

Substitute Professorship at the Institute of Mathematics at Carl von Ossietzky University of Oldenburg.

Summer 2003:

Prof. Dr. Vydas Čekanavičius (University of Vilnius, Lithuania) gave a guest lecture series with the title
Accuracy of approximations in limit theorems. (Abstract.)
Lecture Notes: pages 1 - 109 (revised version, July 2003).

Winter 2001/02:

Der Aktuar in der betrieblichen Altersversorgung:

Hier ist das PDF-File der Präsentation von Dr. Zimmermann auf der Exkursion am 05.02.2002 zu Rüß, Dr. Zimmermann und Partner (GbR) Beratende Aktuare in Hamburg.



Postal address: Please use the new address given above!



Areas of interest:
  • Probability theory, mathematical statistics, and stochastic processes:
    • methods for approximations of probability distributions,
    • compound Poisson approximation and related fields,
    • sums of independent random variables,
    • concentration functions of probability measures,
    • point processes,
    • limit theorems,
    • theory of extreme values, order statistics, and records,
    • approximations in queueing and reliability,
  • insurance and finance mathematics, approximations in the risk theory,
  • theory of complex functions,
  • inequalities.



Preprints and Articles:

(Send me an email for pre- or reprints. There may be essential changes between preprint and published paper.)

[22] Maximal probabilities of convolution powers of discrete uniform distributions. (Jointly with Lutz Mattner).
Submitted, 6 pages, 6 June 2007. Preprint.
[21] A shorter proof of Kanter's Bessel function concentration bound. (Jointly with Lutz Mattner).
Probability Theory and Related Fields, 139(1-2), 191−205, 2007.
Preprint. The original publication is available at www.springerlink.com
[20] Binomial approximation to the Markov binomial distribution. (Jointly with Vydas Čekanavičius).
Acta Applicandae Mathematicae, 96(1--3), 137−146, 2007.
Preprint. The original publication is available at www.springerlink.com.
[19] On variational bounds in the compound Poisson approximation of the individual risk model.
Insurance: Mathematics and Economics, 40(3), 403−414, 2007. Preprint.
[18] An expansion in the exponent for compound binomial approximations. (Jointly with Vydas Čekanavičius).
Lietuvos Matematikos Rinkinys, 46(1), 67−110, 2006.
(See also in: Lithuanian Mathematical Journal, 46(1), 54−91, 2006).
[17] Compound binomial approximations. (Jointly with Vydas Čekanavičius).
Annals of the Institute of Statistical Mathematics, 58(1), 187−210, 2006.
Preprint. The original publication is available at www.springerlink.com.
[16] On Hipp's compound Poisson approximations via concentration functions.
Bernoulli, 11(3), 533−557, 2005. Preprint.
[15] Two-parametric compound binomial approximations. (Jointly with Vydas Čekanavičius).
Lietuvos Matematikos Rinkinys, 44(4), 443−466, 2004.
(See also in: Lithuanian Mathematical Journal, 44(4), 354−373, 2004).
[14] Poisson approximation via the convolution with Kornya-Presman signed measures.
Teoriya Veroyatnostei i ee Primeneniya, 48(3), 628−632, 2003.
(See also in: Theory of Probability and its Applications, 48(3), 555−560, 2003). Preprint.
[13] On error bounds for the approximation of random sums. (Jointly with Dietmar Pfeifer).
Presented at the XXXIV ASTIN Colloquium 2003 of the International Actuarial Association,
24−27 August 2003, Berlin, Germany. Preprint.
[12] Kerstan's method for compound Poisson approximation.
The Annals of Probability, 31(4), 1754−1771, 2003. Preprint.
('Best Paper Award', 2003 Annual Conference of the German Mathematical Society (DMV)).
[11] Poisson approximation of multivariate Poisson mixtures.
Journal of Applied Probability, 40(2), 376−390, 2003.
[10] On the distance between the distributions of random sums. (Jointly with Dietmar Pfeifer).
Journal of Applied Probability, 40(1), 87−106, 2003.
[9] Improvements in the Poisson approximation of mixed Poisson distributions.
Journal of Statistical Planning and Inference, 113(2), 467−483, 2003. Preprint.
[8] Kerstan's method in the multivariate Poisson approximation: an expansion in the exponent.
Teoriya Veroyatnostei i ee Primeneniya, 47(2), 397−402, 2002.
(See also in: Theory of Probability and its Applications, 47(2), 358−363, 2002). Preprint.
[7] Multinomial and Krawtchouk approximations to the generalized multinomial distribution.
Teoriya Veroyatnostei i ee Primeneniya, 46(1), 117−133, 2001.
(See also in: Theory of Probability and its Applications, 46(1), 103−117, 2001). Preprint.
[6] Sharp constants in the Poisson approximation.
Statistics and Probability Letters, 52(2), 155−168, 2001. Preprint.
[5] Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion.
Teoriya Veroyatnostei i ee Primeneniya, 45(2), 328−344, 2000.
(See also in: Theory of Probability and its Applications, 45(2), 258−272, 2000). Preprint.
[4] Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution.
Bernoulli, 5(6), 1021−1034, 1999.
[3] On the rate of multivariate Poisson convergence.
Journal of Multivariate Analysis, 69(1), 120−134, 1999.
[2] Metric multivariate Poisson approximation of the generalized multinomial distribution.
Teoriya Veroyatnostei i ee Primeneniya, 43(2), 404−413, 1998.
(See also in: Theory of Probability and its Applications, 43(2), 306−315, 1998). Preprint.
[1] A semigroup approach to Poisson approximation with respect to the point metric.
Statistics and Probability Letters, 24(4), 305−314, 1995.



Doctoral thesis:

Metrische Poisson-Approximation (Metric Poisson Approximation). (In German). Department of Mathematics, University of Oldenburg, , 186 p., 1996.



Habilitation thesis:

Contributions to the approximation of some important distributions in the risk theory. Department of Mathematics, University of Hamburg, 2002. (Contains the articles 2, 3, 5, 7−12, see above).



Lectures and seminars:

Summer 2007: The Probabilistic Method (Lecture 2+0),
Summer 2006: (Substitute Professorship for Mathematics at the
Institute of Mathematics at Carl von Ossietzky University of Oldenburg)
- Markov Chains (Lecture 3+1),
- Insurance Mathematics II (Lecture 3+1),
- Seminar on Mathematical Stochastics for High School Teachers (at Univ. Hamburg),
Winter 2005/06: (Substitute Professorship ''Stochastics'' at the
Institute of Optimization and Stochastics of Martin-Luther-University of Halle-Wittenberg)
- Mathematical Risk Theory (Lecture 4+2),
- Statistics of Extremes (Lecture 2+0),
Summer 2004: (Substitute Professorship ''Stochastics / Insurance Mathematics'' at the
Mathematical Institute of University of Cologne)
- Stochastic Models in Insurance Mathematics (Lecture 2+2),
Winter 2003/04: (Substitute Professorship ''Probability Theory, particularly Stochastic Processes'' at the
Institute for Mathematical Stochastics of TU Dresden)
- Stochastic Point Processes (on Measurable Spaces), (Lecture 2+0),
- Poisson Approximation (Lecture 2+0),
- Statistics for Communication Scientists (Lecture 2+0),
- Proseminar on Generating Functions,
Summer 2003: (Substitute Professorship ''Insurance Mathematics'' at the
Department of Mathematics of University of Hamburg)
- Insurance Mathematics II (Lecture 3+1),
- Seminar on Mathematical Statistics and Stochastic Processes,
Winter 2002/03: - Insurance Mathematics I (Lecture 3+1),
- Seminar on Insurance Mathematics (Stochastic Orders in Risk Theory),
Summer 2002: - Insurance Mathematics II (Lecture 3+1),
Winter 2001/02: - Mathematical Methods of Risk Theory (Lecture 2+0),
- Seminar on Insurance Mathematics,
Summer 2001: - Insurance Mathematics II (Lecture 3+1),
Winter 2000/01: - Insurance Mathematics I (Lecture 3+1),
- Pension Insurance Mathematics, Part I, (Introduction to Stochastics for Employees of Insurance Companies), (Lecture 2+0), (organized by the Deutsche Aktuar-Akademie),
Winter 1999/00: - Stochastic Processes I (Lecture 4+2),
Summer 1999: - Fractal Structures (Dimension Theory), (Lecture 3+1),
Winter 1998/99: - Statistics of Extremes (Lecture 2+0),
Summer 1998: - Stochastic Point Processes (on Locally Compact Spaces), (Lecture 2+0),
Winter 1997/98: - Mathematical Methods of Risk Theory (Lecture 2+0),
Summer 1997: - Limit Theorems of Probability Theory (Convergence of Probability Measures on Metric Spaces), (Lecture 2+0).



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