Ruin theory with compounding assets - A survey

Insurance: Mathematics and Economics

Volumn 22, Issue 1, 1998, Pages 3-16

  Paulsen, Jostein ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Asymptotic results; Compounded risk process; Diffusion approximation; Exact results; Numerical methods; Probability of absolute ruin; Probability of ruin; Simulation; Upper bounds

Indexed keywords

EID: 0032523393     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(98)00009-2     Document Type: Article

References (40)

1. Asmussen, S., 1984. Approximations for the probability of ruin within finite time. Scandinavian Actuarial Journal, 31-57.
2. Asmussen, S., 1996. Subexponential asymptotics for stochastic processes: extramal behaviour, stationary distributions and first passage probabilities, Working Paper, Department of Statistics, Lund University.
3. Asmussen, S., Bladt, M., 1996. Phase-type distributions and risk processes with state-dependent premiums, Scandinavian Actuarial Journal, 19-36.
4. Asmussen, S., Nielsen, H.M., 1995. Ruin probabilities via local adjustment coefficients, Journal of Applied Probability 32, 736-755.
5. Asmussen, S, Petersen, S.S, 1988. Ruin probabilities expressed in terms of storage processes. Advances of Applied Probability 20, 913-916.
6. Boogaert, P., Crijns, V., 1987. Upperbounds on ruin probabilities in case of negative loadings and positive interest rates. Insurance: Mathematics and Economics 6, 221-232.
7. Dassios, A., Embrechts, P., 1989. Martingales and insurance risk. Communications in Statistics - Stochastic Models 5, 181-217.
8. Delbaen, F., Haezendonck J., 1987. Classical risk theory in an economic environment, Insurance: Mathematics and Economics 6, 85-116.
9. De Vylder, F., 1996. Advanced Risk Theory, Editions de l'Université de Bruxelles.
10. Dickson, D.C.M., Egidio dos Reis, A.D., 1996. The effect of interest on negative surplus. Proceedings of the XXVII Astin colloquium, Copenhagen, Denmark, pp. 337-360.
11. Dickson, D.C.M., Waters, H.R., 1996. Ruin problems: simulation or calculation? British Actuarial Journal 2, 727-740.
12. Dickson, D.C.M., Waters, H.R., 1997. Ruin probabilities with compounding assets. Manuscript.
13. Embrechts, P., Schmidli, H., 1994. Ruin estimation for a general insurance risk model, Advances of Applied Probability 26, 404-422.
14. Furrer, H.J., Schmidli, H., 1994. Exponential inequalities for ruin probabilities of risk processes perturbed by diffusion. Insurance: Mathematics and Economics 15, 23-36.
15. Gerber, H., 1971. Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 71, 63-70.
16. Gerber, H., 1973. Martingales in risk theory, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 73, 205-216.
17. Gjessing, H.K., Paulsen, J., 1997. Present value distributions with applications to ruin theory and stochastic equations. Stochastic Processes and their Applications, 71, 123-144.
18. Harrison, J.M., 1977. Ruin problems with compounding assets, Stochastic Processes and their Applications 5, 67-79.
19. Jacod, J., Shiryaev, A.N. 1987. Limit Theorems for Stochastic Processes, Springer, Berlin.
20. Klüppelberg, C., Stadtmüller, U., 1995. Ruin probabilities in the presence of heavy-tails and interest rates. Scandinavian Actuarial Journal, submitted.
21. Michaud, F., 1996. Estimating the probability of ruin for variable premiums by simulation. Astin Bulletin 26, 93-105.
22. Møller, C.M., 1995. Stochastic differential equations for ruin probabilities. Journal of Applied Probability 32, 74-89.
23. Neuts, M.F., 1981. Matrix-Geometric Solutions in Stochastic Models, Johns Hopkins University Press, Baltimore.
24. Nielsen, H.M., 1994. Generalization of Lundberg Conjugation to Processes with Premiums Depending on the Reserve. Cand. act. dissertation (in Danish). Laboratory of Actuarial Mathematics, University of Copenhagen.
25. Norberg, R., 1996 Ruin problems with assets and liabilities of diffusion type, Working Paper No. 137, Laboratory of Actuarial Mathematics, University of Copenhagen.
26. Paulsen, J., 1993. Risk theory in a stochastic economic environment, Stochastic Processes and their Applications 46, 327-361.
27. Paulsen, J., 1998. Sharp conditions for certain ruin in a risk process with stochastic return on investments, Stochastic Processes and their Applications, to appear.
28. Paulsen, J., Gjessing, H.K. 1997. Ruin theory with stochastic return on investments, Advances in Applied Probability, Advances in Applied Probability 29, 965-985.
29. Petersen, S.S., 1990. Calculation of ruin probabilities when the premium depends on the current reserve, Scandinavian Actuarial Journal, 147-159.
30. Protter, P., 1992. Stochastic Integration and Differential Equations: A New Approach. Springer, Berlin.
31. Ruohonen, M., 1980. On the probability of ruin of risk processes approximated by a diffusion process. Scandinavian Actuarial Journal 113-120.
32. Segerdahl, C.O., 1942. Über einige risikotheoretische Fragestellungen, Skandinavisk Aktuar Tidskrift 25, 43-83.
33. Schmidli, H., 1994a. Risk theory in an economic environment and Markov processes, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Heft 1/1994, 51-70.
34. Schmidli, H., 1994b. Diffusion approximations for a risk process with the possibility of borrowing and investment, Communications in Statistics - Stochastic Models 10, 365-388.
35. Schmidli, H., 1994c. Corrected diffusion approximations for a risk process with the possibility of borrowing and investment, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, Heft 1/1994, 71-81.
36. Siegmund, D., 1979. Corrected diffusion approximation in certain random walk problems, Advances in Applied Probability 11, 701-719.
37. Sundt, B., Teugels, J., 1995. Ruin estimates under interest force, Insurance: Mathematics and Economics 16, 7-22.
38. Sundt, B., Teugels, J., 1997. The adjustment coefficient in ruin estimates under interest force. Insurance: Mathematics and Economics 19, 85-94.
39. Taylor, G.C., 1980. Probability of ruin with variable premium rate, Scandinavian Actuarial Journal, 57-76.
40. Wilkie, A.D., 1986. A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries 39, 341-373.