The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin

Insurance: Mathematics and Economics

Volumn 21, Issue 2, 1997, Pages 129-137

  Gerber, Hans U ^a   Shiu, Elias S W ^b  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Beekman's convolution series; Collective risk theory; Deficit at ruin; Dickson's formula; Duality; Laplace transforms; Lundberg's fundamental equation; Martingales; Optional sampling theorem; Renewal equation; Ruin probability; Surplus process; Time of ruin

Indexed keywords

EID: 0031573355     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(97)00027-9     Document Type: Article

References (17)

1. Beekman, J.A. (1974). Two Stochastic Processes. Almqvist & Wiksell, Stockholm.
2. Cox, D.R. and H.D. Miller (1965). The Theory of Stochastic Processes. Methuen, London.
3. Dickson, D.C.M. (1992). On the distribution of surplus prior to ruin. Insurance: Mathematics and Economics 11, 191-207.
4. Dickson, D.C.M. and A.D. Egídio dos Reis (1994). Ruin problems and dual events Insurance: Mathematics and Economics 14, 51-60.
5. Dufresne, F. and H.U. Gerber (1988). The surpluses immediately before and at ruin, and the amount of the claim causing ruin. Insurance: Mathematics and Economics 7, 193-199.
6. Feller, W. (1971). An Introduction to Probability Theory and Its Applications. Vol. 2, 2nd ed. Wiley, New York.
7. Gerber, H.U. (1979). An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation Monograph Series No. 8. Irwin, Homewood, IL.
8. Gerber, H.U. (1990). When does the surplus reach a given target? Insurance: Mathematics and Economics 9, 115-119.
9. Gerber H.U. and E.S.W. Shiu (1998). On the time value of ruin. North American Actuarial Journal 2 (1), to appear.
10. Kendall, D.G. (1957). Some problems in the theory of dams. Journal of the Royal Statistical Society Series B 19, 207-212.
11. Lundberg, F. (1932). Some supplementary researches on the collective risk theory. Skandinavisk Aktuarietidskrift 15, 137-158.
12. Panjer. H.H. and G.E. Willmot (1992). Insurance Risk Models. Society of Actuaries, Schaumburg, IL.
13. Prabhu, N.U. (1961). On the ruin problem of collective risk theory. Annals of Mathematical Statistics 32, 757-764.
14. Prabhu, N.U. (1980). Stochastic Storage Processes: Queues, Insurance Risk, and Dams. Springer, New York.
15. Resnick, S.I. (1992). Adventures in Stochastic Processes. Birkhäuser, Boston.
16. Seal. H.L. (1969). Stochastic Theory of a Risk Business. Wiley, New York.
17. Takács, L. (1967). Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York. Reprinted by Krieger, Huntington, NY, 1977.