VERSICHERUNGSMATHEMATIK

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Klaus D. Schmidt
Publications
 

 
Actuarial Mathematics     Preprints     Vector Measures and Linear Operators     Embedding theorems for classes of convex sets     Amarts     Mathematics in Engineering     Textbooks     Monographs     Lecture Notes     Diverse Publications    


NEW:

(with Michael Radtke and Anja Schnaus)
Handbook on Loss Reserving.
Springer International Publishing (2016).

(with Markus Dietz and Sebastian Fuchs)
On order statistics and their copulas.
Statistics and Probability Letters 117, 165–172 (2016).

(with Heinz-Willi Goelden, Klaus Th. Hess, Martin Morlock, Klaus J. Schröter)
Schadenversicherungsmathematik
Berlin–Heidelberg: Springer Spektrum (2016).

Stochastische Folgen.
Ein Proseminar mit Anwendungen in der Versicherungsmathematik.
Berlin–Heidelberg: Springer Spektrum (2015).



Actuarial Mathematics

(with Markus Dietz and Sebastian Fuchs)
On order statistics and their copulas.
Statistics and Probability Letters 117, 165–172 (2016).

(with Sebastian Fuchs)
Bivariate copulas: Transformations, asymmetry and measures of concordance.
Kybernetika 50 (1), 109–125 (2014).

On inequalities for moments and the covariance of monotone functions.
Insurance Mathematics and Economics 55, 91–95 (2014).

(with Sebastian Fuchs and Alexander Ludwig)
Zur Exaktheit der Standardformel.
Zeitschrift für die Gesamte Versicherungswissenschaft 102, 87–95 (2013).

(with Siegfried Dietze and Thomas Riedrich)
Marginal–sum equations and related fixed–point problems.
Nonlinear Analysis, Series A: Theory, Methods and Applications, 75, 6088–6102 (2012).

Loss prediction based on run-off triangles.
AStA Adv. Stat. Anal. 96, 265–310 (2012).

Beiträge zur Versicherungsmathematik und Schwerpunktbeitrag Schadenreservierung.
In: Fred Wagner (Hrsg.): Gabler Versicherungslexikon. Wiesbaden: Gabler (2011).

(with Alexander Ludwig)
Gauss-Markov loss prediction in a linear model.
In: Casualty Actuarial Society E-Forum Fall 2010.

(with Kathrin Kloberdanz)
Loss prediction in a linear model under a linear constraint.
AStA Adv. Stat. Anal. 93, 205–220 (2009).

(with Kathrin Kloberdanz)
Prediction in the linear model under a linear constraint.
AStA Adv. Stat. Anal. 92, 207–215 (2008).

(with Mathias Zocher)
The Bornhuetter–Ferguson principle.
Variance 2, 85–110 (2008).

A note on a recent paper by Zaks, Frostig and Levikson.
ASTIN Bull. 37, 319–321 (2007).

(with Klaus Th. Hess)
Risikoteilung und Rückversicherung.
Wiss. Z. TU Dresden 55, 19–23 (2006).

Optimal and additive loss reserving for dependent lines of business.
In: Casualty Actuarial Society Forum Fall 2006, pp. 319–351 (published version, containing misprints).

Methods and models of loss reserving based on run–off triangles: A unifying survey.
In: Casualty Actuarial Society Forum Fall 2006, pp. 269–317 (published version).

(with Klaus Th. Hess and Mathias Zocher)
Multivariate loss prediction in the multivariate additive model.
Insurance: Math. Econom. 39, 185–191 (2006).

(with Mathias Zocher)
Loss reserving and Hofmann distributions.
Mitteilungen SAV, 127–162 (2005).

Optimal quota share reinsurance for dependent lines of business.
Mitteilungen SAV, 173–194 (2004).

(with Klaus Th. Hess)
Optimal premium plans for reinsurance with reinstatements.
ASTIN Bull. 34, 299–313 (2004).

Decision theory.
In: Encyclopedia of Actuarial Science, vol. 1, pp.431–436. New York: Wiley (2004).

Prediction.
In: Encyclopedia of Actuarial Science, vol. 3, pp.1317–1321. New York: Wiley (2004).

(with Michael Radtke) (Eds.)
Handbuch zur Schadenreservierung.
Karlsruhe: Verlag Versicherungswirtschaft (2004, 2012).

Abwicklungsdreiecke.
In: Handbuch zur Schadenreservierung, pp. 7–14. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Abwicklungsmuster.
In: Handbuch zur Schadenreservierung, pp. 15–20. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Additives Verfahren.
In: Handbuch zur Schadenreservierung, pp. 21–24. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Chain–Ladder Verfahren.
In: Handbuch zur Schadenreservierung, pp. 55–64. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Credibility–Modelle – Grundlagen.
In: Handbuch zur Schadenreservierung, pp. 71–80. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Klaus Th. Hess)
Credibility–Modelle – Schadenreservierung.
In: Handbuch zur Schadenreservierung, pp. 81–88. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Holger Lorenz)
Grossing–Up Verfahren.
In: Handbuch zur Schadenreservierung, pp. 93–98. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Kollektives Modell.
In: Handbuch zur Schadenreservierung, pp. 111–114. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Lineare Modelle – Grundlagen.
In: Handbuch zur Schadenreservierung, pp. 115–122. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Lineare Modelle – Schadenreservierung.
In: Handbuch zur Schadenreservierung, pp. 123–130. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Lognormales loglineares Modell – Grundlagen.
In: Handbuch zur Schadenreservierung, pp. 131–134. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Stefan Kaulfuß)
Lognormales loglineares Modell – Schadenreservierung.
In: Handbuch zur Schadenreservierung, pp. 135–139. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Angela Wünsche)
Marginalsummenverfahren.
In: Handbuch zur Schadenreservierung, pp. 145–147. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Klaus Th. Hess and Angela Wünsche)
Multinomial–Modell.
In: Handbuch zur Schadenreservierung, pp. 149–154. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Multiplikative Modelle.
In: Handbuch zur Schadenreservierung, pp. 155–158. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Poisson–Modell.
In: Handbuch zur Schadenreservierung, pp. 163–166. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Klaus Th. Hess and Anja Schnaus)
Sequentielle Modelle.
In: Handbuch zur Schadenreservierung, pp. 189–197. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Michael Radtke and Axel Reich)
Software.
In: Handbuch zur Schadenreservierung, pp. 209–213. Karlsruhe: Verlag Versicherungswirtschaft (2004).

Wahrscheinlichkeitsverteilungen.
In: Handbuch zur Schadenreservierung, pp. 215–222. Karlsruhe: Verlag Versicherungswirtschaft (2004).

(with Klaus Th. Hess and Anett Liewald)
An extension of Panjer's recursion.
ASTIN Bull. 32, 283–297 (2002).

(with Klaus Th. Hess)
A comparison of models for the chain–ladder method.
Insurance: Math. Econom. 31, 351–364 (2002).

A note on the overdispersed Poisson family.
Insurance: Math. Econom. 30, 21–25 (2002).

Versicherungsmathematik.
Berlin–Heidelberg–New York: Springer (2002, 2006, 2009).

(with Klaus Th. Hess)
Credibility–Modelle in Tarifierung und Reservierung.
Allg. Statist. Archiv 85, 225–246 (2001).

Statistical decision problems and linear prediction under vague prior information.
Statistics & Decisions 18, 429–442 (2000).

(with Holger Lorenz)
Grossing–up, chain–ladder and marginal–sum estimation.
Blätter DGVM 24, 195–200 (1999).

Reservierung für Spätschäden: Modellierung am Beispiel des Chain–Ladder–Verfahrens.
Allg. Statist. Archiv 83, 267–280 (1999).

Chain ladder prediction and asset liability management.
Blätter DGVM 24, 1–9 (1999).

Discussion of Halliwell: Loss prediction by generalized least squares.
Proc. Casualty Actuarial Society 86, 736–747 (1999).

Prediction in the linear model: A direct approach.
Metrika 48, 141–147 (1998).

Bayesian models in actuarial mathematics.
Math. Meth. Oper. Res. (ZOR) 48, 117–146 (1998).

(with Angela Wünsche)
Chain ladder, marginal sum and maximum likelihood estimation.
Blätter DGVM 23, 267–277 (1998).

Non–optimal prediction by the chain ladder method.
Insurance: Math. Econom. 21, 17–24 (1997).

Versicherungsmathematik: Prognosen, Formeln und Modelle.
Wiss. Z. TU Dresden 45, 37–40 (1996).

(with Anja Schnaus)
An extension of Mack's model for the chain ladder method.
ASTIN Bull. 26, 247–262 (1996).

Lectures on Risk Theory.
Stuttgart: Teubner (1996).

(with Matthias Timpel)
Experience rating under weighted squared error loss.
Blätter DGVM 22, 289–307 (1995).

Stochastische Modellierung in der Erfahrungstarifierung.
Blätter DGVM 20, 441–455 (1992).

Convergence of Bayes and credibility premiums.
ASTIN Bull. 20, 167–172 (1990).

A note on positive supermartingales in ruin theory.
Blätter DGVM 19, 129–132 (1989).

Positive homogeneity and multiplicativity of premium principles on positive risks.
Insurance: Math. Econom. 8, 315–319 (1989).


 

Preprints

A Note on the Separation Method.
Dresdner Schriften zur Versicherungsmathematik 6/2007.

(with Siegfried Dietze and Thomas Riedrich)
On the Solution of Marginal–Sum Equations.
Dresdner Schriften zur Versicherungsmathematik 1/2006.

(with Carsten Pröhl)
Multivariate chain–ladder.
Dresdner Schriften zur Versicherungsmathematik 3/2005.

(with Matthias Bork)
Optimal reinsurance in the variance model.
Dresdner Schriften zur Versicherungsmathematik 1/2005.

(with Elke Hörnstein and Benjamin Novok–Rostás)
μ–σ–efficient assets in an arbitragefree market.
Dresdner Schriften zur Versicherungsmathematik 1/2004.

Dual optimization of linear and quadratic forms.
Dresdner Schriften zur Versicherungsmathematik 5/2003.

On the covariance of monotone functions of a random variable.
Dresdner Schriften zur Versicherungsmathematik 4/2003.

(with Mathias Zocher)
Claim number processes having the multinomial property.
Dresdner Schriften zur Versicherungsmathematik 1/2003.

A bibliography on loss reserving.  (permanent update)
Dresdner Schriften zur Versicherungsmathematik 4/1999.

(with Klaus Th. Hess)
A note on Poisson renewal processes.  (revised November 25, 2003)
Dresdner Schriften zur Versicherungsmathematik 1/1999.

Stop–loss order revisited.
Dresdner Schriften zur Versicherungsmathematik 4/1998.

Unconditional credibility.
Dresdner Schriften zur Versicherungsmathematik 1/1998.

(with Wolfgang Macht)
Superposition of risk processes.
Dresdner Schriften zur Versicherungsmathematik 3/1995.

(with Klaus Th. Hess and Wolfgang Macht)
Thinning of risk processes.
Dresdner Schriften zur Versicherungsmathematik 1/1995.

(with Klaus Th. Hess)
Experience reserving under vague prior information.
Dresdner Schriften zur Versicherungsmathematik 5/1994.

(with Klaus Th. Hess)
A remark on modelling IBNR claim numbers with random delay pattern.
Dresdner Schriften zur Versicherungsmathematik 4/1994.

(with Klaus Th. Hess)
Convergence of Bayes and credibility premiums in the Bühlmann–Straub model.
Dresdner Schriften zur Versicherungsmathematik 3/1994.


 

Vector Measures and Linear Operators

Decomposition and extension of abstract measures in Riesz spaces.
Rend. Istit. Mat. Univ. Trieste. 29, Suppl. 135–213 (1998).

(with Gerd Waldschaks)
Common extensions of order bounded vector measures.
In: Measure Theory (Oberwolfach 1990). Rend. Circ. Mat. Palermo Serie II 28, Suppl. 117–124 (1992).

(with Gerd Waldschaks)
Common extensions of positive vector measures.
Port. Math. 48, 155–164 (1991).

Daugavet's equation and orthomorphisms.
Proc. Amer. Math. Soc. 108, 905–911 (1990).

A Lebesgue decomposition for vector measures.
In: Methods of Operations Research, vol. 58, pp. 581–582. Frankfurt: Athenäum (1989).

Jordan Decompositions of Generalized Vector Measures.
Pitman Research Notes in Mathematics Series, vol. 214. Essex: Longman (1989).

On the modulus of L– and M–weakly compact operators.
Proc. Kon. Nederl. Akad. Wet. Ser. A 91, 89–92 (1988).

On the modulus of weakly compact operators and strongly additive vector measures.
Proc. Amer. Math. Soc. 102, 862–866 (1988).

Minimal clans: A class of ordered partial semigroups including Boolean rings and lattice–ordered groups.
In: Semigroups – Theory and Applications (Oberwolfach 1986). Lecture Notes in Mathematics, vol. 1320, pp. 300–341. Berlin–Heidelberg–New York: Springer 1988.

Decompositions of vector measures in Riesz spaces and Banach lattices.
Proc. Edinburgh Math. Soc. 29, 23–39 (1986).

A common abstraction of Boolean rings and lattice ordered groups.
Comp. Math. 54, 51–62 (1985).

Decompositions of vector measures.
In: Methods of Operations Research, vol. 50, pp. 389–400. Königstein: Hain (1985).

On the Jordan decomposition for vector measures.
In: Probability in Banach Spaces IV (Oberwolfach 1982). Lecture Notes in Mathematics, vol. 990, pp. 198–203. Berlin–Heidelberg–New York: Springer (1983).

On a result of Cobzas on the Hahn decomposition.
Archiv Math. 39, 564–567 (1982).

A general Jordan decomposition.
Archiv Math. 38, 556–564 (1982).


 

Embedding theorems for classes of convex sets

Embedding theorems for intervals.
Z. Angew. Math. Mech. 67, T 448 – T 449 (1987).

Embedding theorems for cones and applications to classes of convex sets occurring in interval mathematics.
In: Interval Mathematics (Freiburg 1985). Lecture Notes in Computer Science, vol. 212, pp. 159–173. Berlin–Heidelberg–New York: Springer (1986).

Embedding theorems for classes of convex sets in a hypernormed vector space.
Analysis 6, 57–96 (1986).

Embedding theorems for classes of convex sets.
Acta Appl. Math. 5, 209–237 (1986); 11, 295 (1988).

On Rådström's embedding theorem in a hypernormed vector space.
In: Methods of Operations Research, vol. 53, pp. 159–170. Königstein: Hain (1986).

On Rådström's embedding theorem.
In: Methods of Operations Research, vol. 46, pp. 335–338. Königstein: Athenäum/Hain (1983).


 

Amarts

The lattice property of uniform amarts.
Ann. Probability 17, 372–378 (1989).

A sequential Lebesgue–Radon–Nikodym theorem and the Lebesgue decomposition of martingales.
In: Information Theory, Statistical Decision Functions, Random Processes – Transactions of the Tenth Prague Conference (Prague 1986), vol. B, pp. 285–292. Dordrecht: Reidel (1988).

The Andersen–Jessen theorem revisited.
Math. Proc. Cambridge Phil. Soc. 102, 351–361 (1987).

(with Allan Gut)
Amarts and Set Function Processes.
Lecture Notes in Mathematics, vol. 1042. Berlin–Heidelberg–New York: Springer (1983).

Generalized martingales and set function processes.
In: Methods of Operations Research, vol. 44, pp. 167–178. Königstein: Athenäum/Hain (1981).

On the convergence of a bounded amart and a conjecture of Chatterji.
J. Multivariate Anal. 11, 58–68 (1981).

Théorèmes de convergence pour les amartingales en processus de fonctions d'ensembles à valeurs dans un espace de Banach.
C. R. Acad. Sci. Paris Sér. A 290, 1103–1106 (1980).

Théorèmes de structure pour les amartingales en processus de fonctions d'ensembles à valeurs dans un espace de Banach.
C. R. Acad. Sci. Paris Sér. A 290, 1069–1072 (1980).

On the value of a stopped set function process.
J. Multivariate Anal. 10, 123–134 (1980).

Sur la convergence d'une amartingale bornéee et un théorème de Chatterji.
C. R. Acad. Sci. Paris Sér. A 289, 181–183 (1979).

Espaces vectoriels réticulés, décompositions de Riesz, et caractérisations de certains processus de fonctions d'ensembles.
C. R. Acad. Sci. Paris Sér. A 289, 75–78 (1979).

Sur la valeur d'un processus de fonctions d'ensembles.
C. R. Acad. Sci. Paris Sér. A 288, 431–434 (1979).

Sur l'espérance d'une semiamartingale arrêtée.
C. R. Acad. Sci. Paris Sér. A 287, 663–665 (1978).


 

Mathematics in Engineering

(with Sebastian W. Bauer)
Irregular–grid finite–difference simulation of Lake Geneva surge.
J. Hydraulic Eng. 109, 1285–1297 (1983).


 

Textbooks

Stochastische Folgen.
Ein Proseminar mit Anwendungen in der Versicherungsmathematik.
Berlin–Heidelberg: Springer Spektrum (2015).

Maß und Wahrscheinlichkeit.
Berlin–Heidelberg–New York: Springer (2009, 2011).

Versicherungsmathematik.
Berlin–Heidelberg–New York: Springer (2002, 2006, 2009).

(with Klaus Th. Hess and Wolfgang Macht)
Arbeitsbuch Mathematik: Multiple–Choice–Aufgaben.
Berlin–Heidelberg–New York: Springer (2000, 2005).

Mathematik – Grundlagen für Wirtschaftswissenschaftler.
Berlin–Heidelberg–New York: Springer (1998, 2000).


 

Monographs

(with Michael Radtke and Anja Schnaus)
Handbook on Loss Reserving.
Springer International Publishing (2016).

(with Heinz-Willi Goelden, Klaus Th. Hess, Martin Morlock, Klaus J. Schröter)
Schadenversicherungsmathematik
Berlin–Heidelberg: Springer Spektrum (2016).

(with Michael Radtke) (Eds.)
Handbuch zur Schadenreservierung.
Karlsruhe: Verlag Versicherungswirtschaft (2004, 2012).

Lectures on Risk Theory.
Stuttgart: Teubner (1996).

Jordan Decompositions of Generalized Vector Measures.
Pitman Research Notes in Mathematics Series, vol. 214. Essex: Longman (1989).

(with Allan Gut)
Amarts and Set Function Processes.
Lecture Notes in Mathematics, vol. 1042. Berlin–Heidelberg–New York: Springer (1983).


 

Lecture Notes

Conditioning and Prediction.
Modèles et Méthodes de Réservation.
Petit Cours donné à l'Université de Strasbourg en Mai 2003.


 

Diverse Publications

(with Jens Bartenwerfer, Gert Buse, Christian Diepold, Ingelore Döring, Thomas Hörnemann, Bernd Jäger, Daniel John, Marco Lonsing, Klaus-Peter Mangold, Heinz Matitschka, Gerd Romund, Gerd Ulrich Stienen)
Methoden zur Schätzung von Schaden- und Prämienrückstellungen in der Kompositversicherung
GDV 2008, 2011 Überarbeitete Fassung

(with Franz Baier, Gert Buse, Olaf Ermert, Dietmar Kohlruss, Markus Müller, Stefan Oecking, Michael Radtke, Axel Reich, Helmut Valenta)
Software für die aktuarielle Bewertung von Versicherungsportefeuilles.
Der Aktuar 10, 7–12 (2004).

Mathematik und Wirtschaft – eine Herausforderung.
ibv 9/99, 565–569 (1999).

(with Christine Sänger)
Wirtschaftsmathematik und verwandte Studiengänge – Ergebnisse einer Umfrage 1998.
Technische Universität Dresden, Fachrichtung Mathematik (1998).
 

C. Weber, 28.01.2016