Advertisement

Reflection Strategies

  • Andreas E. Kyprianou
Chapter
Part of the EAA Series book series (EAAS)

Abstract

We to the first of the three cases in which the path of the Cramér–Lundberg process is perturbed through the payments of dividends. Recall that a reflection (or barrier) strategy consists of paying dividends out of the surplus in such a way that, for a fixed barrier a>0, any excess of the surplus above this level is instantaneously paid out. The key object of interest in this chapter is the present value of the dividends paid until ruin under force of interest.

Keywords

Arrival Rate Scale Function Spatial Homogeneity Compound Poisson Process Positive Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Albrecher, H., Gerber, H.: A note on moments of dividends. Acta Mathematica Applicatae Sinica 27, 353–354 (2011) MathSciNetCrossRefGoogle Scholar
  2. Bertoin, J., Yor, M.: Exponential functionals of Lévy processes. Probab. Surv. 2, 191–212 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  3. Cohen, S., Kuznetsov, A., Kyprianou, A.E., Rivero, V.: Lévy Matters II. Lecture Notes in Mathematics, vol. 2061. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  4. Dickson, D.C.M., Waters, H.R.: Some optimal dividends problems. Astin Bull. 34, 49–74 (2004) MathSciNetCrossRefzbMATHGoogle Scholar
  5. Gerber, H.U.: Entscheidungskriterien für den zusammengesetzten Poisson-Prozess. Schweiz. Verein. Versicherungsmath. Mitt. 69, 185–228 (1969) zbMATHGoogle Scholar
  6. Gerber, H.U.: Games of economic survival with discrete and continuous income processes. Operations Research 20, 37–45 (1972) CrossRefzbMATHGoogle Scholar
  7. Greenwood, P.E., Pitman, J.W.: Fluctuation identities for Lévy processes and splitting at the maximum. Adv. Appl. Probab. 12, 839–902 (1980) MathSciNetGoogle Scholar
  8. Itô, K.: Poisson point processes attached to Markov processes. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability Theory, pp. 225–239. University of California Press, Berkeley (1972) Google Scholar
  9. Kingman, J.F.C.: Poisson Processes. Oxford University Press, Oxford (1993) zbMATHGoogle Scholar
  10. Kyprianou, A.E., Palmowski, Z.: Distributional study of de Finetti’s dividend problem for a general Lévy insurance risk process. J. Appl. Probab. 44, 428–443 (2007) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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) MathSciNetCrossRefzbMATHGoogle Scholar
  12. Renaud, J.-F., Zhou, X.: Moments of the expected present value of total dividends until ruin in a Lévy risk model. J. Appl. Probab. 44, 420–427 (2007) MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Andreas E. Kyprianou
    • 1
  1. 1.Department of Mathematical SciencesUniversity of BathBathUnited Kingdom

Personalised recommendations