Phase-type distributions and risk processes with state-dependent premiums

Scandinavian Actuarial Journal

Volumn 1996, Issue 1, 1996, Pages 19-36

  Asmussen, Søren ^a   Bladt, Mogens ^b  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Differential equations; Numerical methods; Phase type distributions; Random environment; Ruin probability

Indexed keywords

EID: 0001911405     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461238.1996.10413960     Document Type: Article

References (20)

1. Sparre Andersen, E. (1957). On the collective theory of risk in the case of contagagion between the claims. Transactions XVth International Congress of Actuaries, New York, 2, 219-229.
2. Asmussen, S. (1987). Applied Probability and Queues. John Wiley & Sons, Chichester, NewYork.
3. Asmussen, S. (1995). Ruin Probabilities. World Scientific PublishingCo., Singapore (to appear).
4. Asmussen, S., Frey, A., Rolski, T. & Schmidt, V. (1994). Does Markov-modulation increase the risk? To appear in ASTIN Bull.
5. Asmussen, S. & Nielsen, H. M. (1995). RuinProbabilities via localadjustment coefficients. To appear in J. Appl. Probab. (Dec. 1995).
6. Asmussen, S. & Schock Petersen, S. (1989). Ruin probabilities expressed in terms of storage processes. Adv. Appl. Probab. 20, 913-916.
7. Asmussen, S. & Rolski, T. (1991). Computational methods in risk theory: A matrix-algorithmic approach. Insurance: Mathematics and Economics 10, 259-274.
8. Baker, C. T. H. (1977). The Numerical Solution of Integral Equations. Clarendon Press, Oxford.
9. Bladt, M. (1993). Ph.D. thesis, Aalborg University, Denmark.
10. Cramer, H. (1930). On the Mathematical Theory of Risk. Skandia Jubilee Volume, Stockholm.
11. Emanuel, D. C., Harrison, J. M. & Taylor, A. J. (1975). A diffusion approximation for the ruin probability with compounding assets. Scand. Actuarial J., 37-45.
12. Feller, W. (1971). An Introduction to Probability Theory and its Applications. Vol. 2. 2nd ed. John Wiley & Sons, New York.
13. Gerber, H. (1971). Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Mitt. Verein Schweitz. Versieh. Math. 71, 63-70.
14. Gerber, H. (1979). An Introduction to the Mathematical Risk Theory. S. S. Huebner Foundation Monographs, University of Pennsylvania.
15. Graham, A. (1981). Kronecker Products and Matrix Calculus with Applications. Ellis Horwood Series, London.
16. Grandeil, J. (1991). Aspects of Risk Theory. Springer Verlag, New York. Ellis Horwood Series, London.
17. Harrison, J. M. (1977). Ruin problems with compounding assets. Stoch. Proc. Appl., 5, 67-79.
18. Neuts, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore and London.
19. Schock Petersen, S. (1990). Calculation of ruin probabilities when the premium depends on the current reserve. Scand. Actuarial J 147-159.
20. Taylor, G. C. (1980). Probability of ruin with variable premium rate. Scand. Act. J 57-76.