nach oben

Erschienen in:

2013 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : Andreas E. Kyprianou

Erschienen in: Gerber–Shiu Risk Theory

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this brief introductory chapter, we outline the basic context of these lecture notes. In particular, we explain what we understand by so-called Gerber–Shiu theory and the role that it has played in classical ruin theory.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nächstes Kapitel The Wald Martingale and the Maximum

Henceforth written i.i.d. for short.

We assume that the reader is familiar with the basic theory of Markov processes and, in particular, the use of the (strong) Markov property.

Throughout this text, we use the standard definition inf∅:=∞.

See the historical remarks at the end of this chapter.

Albrecher, H., Borst, S., Boxma, O., Resing, J.: Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models. J. Appl. Probab. 48A, 3–14 (2011) MathSciNetCrossRefMATH

Albrecher, H., Hipp, C.: Lundberg’s risk process with tax. Blaetter der DGVFM 28, 13–28 (2007) MathSciNetCrossRefMATH

Albrecher, H., Renaud, J.-F., Zhou, X.: A Lévy insurance risk process with tax. J. Appl. Probab. 45, 363–375 (2008) MathSciNetCrossRefMATH

Asmussen, S., Albrecher, H.: Ruin Probabilities, 2nd edn. Advanced Series on Statistical Science & Applied Probability, vol. 14. World Scientific, Hackensack (2010) MATH

Asmussen, S., Taksar, M.: Controlled diffusion models for optimal dividend pay-out. Insurance Math. Econom. 20, 1–15 (1997) MathSciNetCrossRefMATH

Avram, F., Palmowski, Z., Pistorius, M.R.: On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Probab. 17, 156–180 (2007) MathSciNetCrossRefMATH

Azcue, P., Muler, N.: Optimal reinsurance and dividend distribution policies in the Cramér–Lundberg model. Math. Finance 15, 261–308 (2005) MathSciNetCrossRefMATH

Cramér, H.: Collected Works, vol. I. Edited and with a preface by Anders Martin-Löf. Springer, Berlin (1994a) MATH

Cramér, H.: Collected Works, vol. II. Edited and with a preface by Anders Martin-Löf. Springer, Berlin (1994b) MATH

de Finetti, B.: Su un’impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries 2, 433–443 (1957)

Dickson, D.C.M.: Insurance Risk and Ruin. Cambridge University Press, Cambridge (1999)

Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance. Springer, Berlin (1997) CrossRefMATH

Feller, W.: An Introduction to Probability Theory and Its Applications, vol II, 2nd edn. Wiley, New York (1971) MATH

Gerber, H.U.: Entscheidungskriterien für den zusammengesetzten Poisson-Prozess. Schweiz. Verein. Versicherungsmath. Mitt. 69, 185–228 (1969) MATH

Gerber, H.U.: Games of economic survival with discrete and continuous income processes. Operations Research 20, 37–45 (1972) CrossRefMATH

Gerber, H.U., Shiu, E.S.W.: The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance Math. Econom. 21, 129–137 (1997) MathSciNetCrossRefMATH

Gerber, H.U., Shiu, E.S.W.: On the time value of ruin. North Am. Actuar. J. 2, 48–78 (1998) MathSciNetCrossRefMATH

Gerber, H.U., Shiu, E.S.W.: On optimal dividend strategies in the compound Poisson model. North Am. Actuar. J. 10, 76–93 (2006b) MathSciNetCrossRef

Jeanblanc, M., Shiryaev, A.N.: Optimization of the flow of dividends. Russian Math. Surveys 50, 257–277 (1995) MathSciNetCrossRefMATH

Kallenberg, O.: Foundations of Modern Probability, 2nd edn. Probability and Its Applications. Springer, New York (2002) MATH

Kyprianou, A.E., Loeffen, R.L., Pérez, J.L.: Optimal control with absolutely continuous strategies for spectrally negative Lévy processes. J. Appl. Probab. 49, 150–166 (2012) MathSciNetCrossRefMATH

Kyprianou, A.E., Ott, C.: Spectrally negative Lévy processes perturbed by functionals of their running supremum. J. Appl. Probab. 49, 1005–1014 (2012) MathSciNetCrossRefMATH

Kyprianou, A.E., Zhou, X.: General tax structures and the Lévy insurance risk model. J. Appl. Probab. 46, 1146–1156 (2009) MathSciNetCrossRefMATH

Kyprianou, A.E., Rivero, V., Song, R.: Convexity and smoothness of scale functions and de Finetti’s control problem. J. Theoret. Probab. 23, 547–564 (2010) MathSciNetCrossRefMATH

Loeffen, R.L.: On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes. Ann. Appl. Probab. 18, 1669–1680 (2008) MathSciNetCrossRefMATH

Loeffen, R.L., Renaud, J.-F.: De Finetti’s optimal dividends problem with an affine penalty function at ruin. Insurance Math. Econom. 46, 98–108 (2010) MathSciNetCrossRefMATH

Lundberg, F.: Approximerad Framställning Av Sannolikhetsfunktionen. Återförsäkring Av Kollektivrisker. Akad. Afhandling. Almqvist. och Wiksell, Uppsala (1903)

Schmidli, H.: Stochastic Control in Insurance. Probability and Its Applications. Springer, London (2008) MATH

Titel: Introduction
verfasst von: Andreas E. Kyprianou
Verlag: Springer International Publishing
Buch: Gerber–Shiu Risk Theory
Print ISBN: 978-3-319-02302-1

Electronic ISBN: 978-3-319-02303-8

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-3-319-02303-8_1