Approximations for the Gerber-Shiu expected discounted penalty function in the compound Poisson risk model

Advances in Applied Probability

Volumn 39, Issue 2, 2007, Pages 385-406

  Pitts, Susan M ^a   Politis, Konstadinos ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF PIRAEUS   (Greece)

Author keywords

Defective renewal equation; Deficit at ruin; Functional approach; Surplus prior to ruin; Time of ruin

Indexed keywords

FUNCTION EVALUATION; MATHEMATICAL MODELS; POISSON DISTRIBUTION; SIZE DISTRIBUTION;

DEFECTIVE RENEWAL EQUATION; PENALTY FUNCTION; TIME OF RUIN;

APPROXIMATION THEORY;

EID: 34548022134     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1183667616     Document Type: Article

References (21)

1. ASMUSSEN, S. (2000). Ruin Probabilities. World Scientific, Singapore.
2. CARTAN, H. (1971). Differential Calculus. Hermann, Paris.
3. CHENG, Y. AND TANG, Q. (2003). Moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. N. Amer. Actuarial J. 7, 1-12.
4. DICKSON, D. C. M AND HIPP, C. (2001). On the time to ruin for Erlang(2) risk processes. Insurance Math. Econom. 29, 333-344.
5. DREKIC, S., DICKSON, D. C. M., STANFORD, D. A. AND WILLMOT, G. E. (2004). On the distribution of the deficit at ruin when claims are phase-type. Scand. Actuarial J. 2004, 105-120.
6. DUFRESNE, D. (2006). Fitting combinations of exponentials to probability distributions. Appl. Stoch. Models Business Industry 23, 23-48.
7. DUNFORD, N. AND SCHWARTZ, J. T. (1958). Linear Operators. Part I. General Theory. John Wiley, New York.
8. GERBER, H. U. AND SHIU, E. S. W. (1998). On the time value of ruin. N. Amer. Actuarial J. 2, 48-78.
9. GERBER, H. U. AND SHIU, E. S. W. (2005). The time value of ruin in a Sparre Andersen model. N. Amer. Actuarial J. 2, 49-84.
10. GERBER, H. U., GOOVAERTS, M. J. AND KAAS, R. (1987). On the probability and severity of ruin. ASTIN Bull. 17, 151-163.
11. GRÜBEL, R. (1989). Stochastic models as functionals: some remarks on the renewal case. J. Appl. Prob. 26, 296-303.
12. GRÜBEL, R. AND PITTS, S. M. (1992). A functional approach to the stationary waiting time and idle period distributions of the GI/G /1 queue. Ann. Prob. 20, 1754-1778.
13. LI, S. AND GARRIDO, J. (2004). On ruin for the Erlang(n) risk process. Insurance Math. Econom. 34, 391-408.
14. LIN, X. S. AND WILLMOT, G. E. (1999). Analysis of a defective renewal equation arising in ruin theory. Insurance Math. Econom. 25, 63-84.
15. LIN, X. S. AND WILLMOT, G. E. (2000). The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance Math. Econom. 27, 19-44.
16. PITTS, S. M. (1998). A functional approach to approximations for the observed open times in single ion channels. J. Math. Anal. Appl. 219, 260-278.
17. PITTS, S. M. (1999). Approximations for semi-Markov single ion channel models. In Semi-Markov Models and Applications, eds J. Janssen and N. Limnios, Kluwer, Dordrecht, pp. 103-115.
18. PITTS, S. M. (2004). A functional approach to approximations for the individual risk model. ASTIN Bull. 34, 379-397.
19. POLITIS, K. AND PITTS, S. M. (1998). Approximations for solutions of renewal-type equations. Stoch. Process. Appl. 78, 195-216.
20. RUDIN, W. (1986). Real and Complex Analysis. McGraw-Hill, New York.
21. WILLMOT, G. E. AND LIN, X. S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications. Springer, New York.