Complete monotonicity of the probability of ruin and de Finetti’s dividend problem

1. R. Loeffen, On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes, The Annals of Applied Probability, 2008, 18(5): 1669–1680.

   Article  MathSciNet  MATH  Google Scholar 

2. S. Asmussen, Ruin Probabilities, World Scientific, Singapore, 2000.

   Book  Google Scholar 

3. T. Rolski, H. Schmidli, V. Schmidt and J. Teugels, Stochastic Processes for Insurance and Finance, New York, Wiley, 1999.

   Book  MATH  Google Scholar 

4. G. E. Willmot and X. S. Lin, Lundberg Approximations for Compound Distributions with Insurance Applications, New York, Springer, 2001.

   Book  Google Scholar 

5. M. Brown, Further monotonicity properties for specialized renewal processes, The Annals of Probability, 1981, 9: 891–895.

   Article  MathSciNet  MATH  Google Scholar 

6. D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, Cambridge, 2004.

   Book  MATH  Google Scholar 

7. M. Bagnoli and T. Bergstrom, Log-concave probability and its applications, Economic Theory, 2005, 26: 445–469.

   Article  MathSciNet  MATH  Google Scholar 

8. D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941.

   Google Scholar 

9. J. Keilson, Exponential spectra as a tool for the study of serves systems with several classes of customers, Journal of Applied Probability, 1978, 15: 162–170.

   Article  MathSciNet  MATH  Google Scholar 

10. R. Szekli, On the concavity of the waiting time distribution in some GI/G/1 queues, Journal of Applied Probability, 1986, 23: 555–561.

    Article  MathSciNet  MATH  Google Scholar 

11. J. G. Shanthikumar, DFR properties of first-passage times and its preservation under geometric compounding, The Annals of Probability, 1988, 33: 397–406.

    Article  MathSciNet  Google Scholar 

12. F. Dufresne and H. U. Gerber, Risk theory for the compound Poission process that is perturbed by diffusion, Insurance: Mathematics and Economics, 1991, 10: 51–59.

    Article  MathSciNet  MATH  Google Scholar 

13. G. Gripenberg, On positive, nonincreasing resolvents of Volterra equations, Journal Differential Equations, 1978, 30: 380–390.

    Article  MathSciNet  MATH  Google Scholar 

14. F. Avram, Z. Palmowski and M. R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, The Annals of Applied Probability, 2007, 17: 156–180.

    Article  MathSciNet  MATH  Google Scholar 

15. H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal, 1998, 2(1): 48–78.

    MathSciNet  MATH  Google Scholar 

16. H. U. Gerber and E. S. W. Shiu, Optimal dividends: analysis with Brownian motion, North American Actuarial Journal, 2004, 8: 1–20.

    MathSciNet  MATH  Google Scholar 

17. H. U. Gerber, X. S. Lin and H. Yang, A note on the dividends-penalty identity and the optimal dividend barrier, Astin Bulletin, 2006, 36: 489–503.

    Article  MathSciNet  MATH  Google Scholar 

18. S. M. Li, The distribution of the dividend payments in the compound Poission risk model perturbed by diffusion, Scandinavian Actuarial Journal, 2006, (2): 73–85.

19. H. U. Gerber, Entscheidungskriterien für den zusammengesetzten Poisson-Prozess, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 1969, 69: 185–227.

    Google Scholar 

20. H. Albrecher and S. Thonhauser, Optimal dividend strategies for a risk process under force of interest, Insurance: Mathematics and Economics, 2008, 43: 134–149.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

22. B. Chan, H. U. Gerber and E. S. W. Shiu, Discussion of “on a classical risk model with a constant dividend barrier”, North American Actuarial Journal, 2006, 10(2): 133–139.

    MathSciNet  Google Scholar 

23. H. U. Gerber, E. S. W. Shiu and N. Smith, Methods for estimating the optimal dividend barrier and the probability of ruin, Insurance: Mathematics and Economics, 2008, 42: 243–254.

    Article  MathSciNet  MATH  Google Scholar 

Download references