On the ruin probabilities in a general economic environment

Stochastic Processes and their Applications

Volumn 83, Issue 2, 1999, Pages 319-330

  Nyrhinen, Harri ^a  

^a NONE

Author keywords

Insurance mathematics; Large deviations theory; Level crossing probability; Ruin problem; Stochastic discounting

Indexed keywords

EID: 0033211535     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00030-7     Document Type: Article

References (20)

1. Asmussen, S., Bladt, M., 1996. Phase-type distributions and risk processes with state-dependent premiums. Scand. Actuarial J. 19-36.
2. Bühlmann, H., 1967. Experience rating and credibility. Astin Bull. 4, 199-207.
3. Daykin, C.D., Pentikäinen, T., Pesonen, M., 1994. Practical Risk Theory for Actuaries. Chapman and Hall, London.
4. Dembo, A., Zeitouni, O., 1993. Large Deviations Techniques and Applications. Jones and Bartlett Publishers, Boston.
5. Gjessing, H.K., Paulsen, J., 1997. Present value distributions with applications to ruin theory and stochastic equations. Stochastic Process. Appl. 71, 123-144.
6. Goldie, C.M., 1991. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1, 126-166.
7. Iscoe, I., Ney, P., Nummelin, L., 1985. Large deviations of uniformly recurrent Markov additive processes. Adv. Appl. Math. 6, 373-412.
8. Martin-Löf, A., 1983. Entropy estimates for ruin probabilities. In: Gut, A., Holst, L. (Eds.), Probability and Mathematical Statistics. Dept. of Mathematics, Uppsala University, pp. 129-139.
9. Martin-Löf, A., 1986. Entropy, a useful concept in risk theory. Scand. Actuarial J. 223-235.
10. Møller, C.M., 1995. Stochastic differential equations for ruin probabilities. J. Appl. Probab. 32, 74-89.
11. Nyrhinen, H., 1994. Rough limit results for level-crossing probabilities. J. Appl. Probab. 31, 373-382.
12. Nyrhinen, H., 1998. Rough descriptions of ruin for a general class of surplus processes. Adv. Appl. Probab. 30, 1008-1026.
13. Paulsen, J., 1993. Risk theory in a stochastic economic environment. Stochastic Process. Appl. 46, 327-361.
14. Paulsen, J., 1998a. Sharp conditions for certain ruin in a risk process with stochastic return on investments. Stochastic Process. Appl. 75, 135-148.
15. Paulsen, J., 1998b. Ruin theory with compounding assets - A survey. Insurance: Math. and Econom. 22, 3-16.
16. Paulsen, J., Gjessing, H.K., 1997. Ruin theory with stochastic return on investments. Adv. Appl. Probab. 29, 965-985.
17. Rockafellar, R.T., 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
18. Ruohonen, M., 1980. On the probability of ruin of risk processes approximated by a diffusion process. Scand. Actuarial J. 113-120.
19. Schnieper, R., 1983. Risk processes with stochastic discounting. Mitt. Verein. Schweiz. Vers. Math. 83 Heft 2, 203-218.
20. Wilkie, A.D., 1986. A stochastic investment model for actuarial use. Trans. Faculty Actuaries 39, 341-373.