Risk theory in a markovian environment

Scandinavian Actuarial Journal

Volumn 1989, Issue 2, 1989, Pages 69-100

  Asmussen, Søren ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857400003     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461238.1989.10413858     Document Type: Article

References (57)

1. Arjas, E. (1972). On the use of fundamental identity in the theory of semi-Markov processes. Adv. Appl. Probab. 4, 271-284.
2. Arjas, E. & Speed, T. P. (1973). Symmetric Wiener-Hopf factorisations in Markov additive processes. Z. Wahrscheinlichkeitsth. verw. Geb. 26, 105-118.
3. Arjas, E. & Speed, T. P. (1973). Topics in Markov additive processes. Math. Scand. 33, 171-192.
4. Arndt, K. (1980). Asymptotic properties of the distribution of the supremum of a random walk on a Markov chain. Th. Probab. Appl. 25, 309-324.
5. Arndt, K. (1981). On properties of boundary functionals of a random walk on a Markov chain. Math. Operationsforschung Statist. 12, 85-100.
6. Arndt, K. (1984). On the distribution of the supremum of a random walk on a Markov chain. Limit Theorems and Related Problems (ed. A. A. Borovkov), pp. 253-267. Optimizations Software Inc., New York.
7. Asmussen, S. (1984). Approximations for the probability of ruin within finite time. Scand. Actuarial J., 31-57.
8. Asmussen, S. (1985). Approximations for the probability of ruin within finite time. Scand. Actuarial J., 64.
9. Asmussen, S. (1985). Conjugate processes and the simulation of ruin problems. Stoch. Proc. Appl. 20, 213-229.
10. Asmussen, S. (1987). Applied probability and queues. John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore.
11. Asmussen, S. (1987). The heavy traffic limit of a class of Markovian queuing models. Opns. Res. Letters 6, 301-306.
12. Asmussen, S. (1989). Aspects of matrix Wiener Hopf factorisation in applied probability. The Mathematical Scientist (in print).
13. Asmussen, S. (1989). Ladder heights and the Markov-modulated M/G/1 queue. In preparation.
14. Asmussen, S. & Schock Petersen, S. (1988). Ruin probabilities expressed in terms of storage processes. Adv. Appl. Probab. 20, 913-916.
15. Asmussen, S. & Thorisson, H. (1988). Large deviation results for time-dependent queue length probabilities. Stochastic Models 4, 99-116.
16. Bellman, R. (1957). On a generalization of the fundamental identity of Wald. Proc. Camb. Philos. Soc. 53, 257-259.
17. Björk, T. & Grandell, J. (1988). Exponential inequalities for ruin probabilities in the Cox case. Scand. Actuarial J., 77-111.
18. Borovkov, K. A. (1980). Stability theorems and estimates of the rate of convergence of the components of factorizations for walks defined on Markov chains. Th. Probab. Appl. 25, 325-334.
19. Davies, B. & Martin, B. (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. J. Comp. Phys. 33, 1-32.
20. Feller, W. (1971). An introduction to probability theory and its applications, II (2nd ed.). Wiley, New York.
21. Grandell, J. (1977/78). A class of approximations of ruin probabilities. Scand. Act. J., Suppl. 1977, 37-52; Scand. Act. J. 1978, 77-78.
22. Hunter, J. J. (1982). Generalized inverses and their application to applied probability problems. Linear Algebra Appl. 45, 157-198.
23. Höglund, T. (1974). Central limit theorems and statistical inference for finite Markov chains. Z. Wahrscheinlichkeitsth. verw. Geb. 29, 123-151.
24. Höglund, T. (1986). The ruin problem for finite Markov chains. Technical report.
25. Janssen, J. (1970). Sur une généralisation du concept de promenade aléatoire sur la droite réelle. Ann. Inst. H. Poincaré, B, VI, 249-269.
26. Janssen, J. (1980). Some transient results on the M/SM/1 special semi-Markov model in risk and queuing theories. Astin Bull. 11, 41-51.
27. Janssen, J. & Reinhard, J. M. (1985). Probabilités de ruine pour une classe de modeles de risque semi-Markoviens. Astin Bull. 15, 123-133.
28. Keilson, J. (1979). Markov chain models-rarity and exponentiality. Springer-Verlag, New York, Heidelberg, Berlin.
29. Keilson, J. & Wishart, D. M. G. (1964). A central limit theorem for processes defined on a finite Markov chain. Proc. Camb. Philos. Soc. 60, 547-567.
30. Keilson, J. & Wishart, D. M. G. (1965). Boundary problems for additive processes defined on a finite Markov chain. Proc. Camb. Philos. Soc. 61, 173-190.
31. Keilson, J. & Wishart, D. M. G. (1967). Addenda to processes defined on a finite Markov chain. Proc. Camb. Philos. Soc. 63, 187-193.
32. Kemeny, J. G., Snell, J. L., Knapp, A. W. & Griffeaths, D. (1976). Denumerable Markov chains. Springer-Verlag, New York, Heidelberg, Berlin.
33. Kemperman, J. H. B. (1961). The passage problem for a Markov chain. University of Chicago Press, Chicago.
34. Kingman, J. F. C. (1961). A convexity property of positive matrices. Quart. J. Math. Oxford 12, 283-284.
35. Miller, H. D. (1961). A generalization of Wald’s identity with applications to random walks. Ann. Math. Statist. 32, 549-560.
36. Miller, H. D. (1961). A convexity property in the theory of random variables defined on a finite Markov chain. Ann. Math. Statist. 32, 1260-1270.
37. Miller, H. D. (1962). A matrix factorization problem in the theory of random variables defined on a finite Markov chain. Proc. Camb. Philos. Soc. 58, 268-285.
38. Miller, H. D. (1962). Absorption probabilities for sums of random variables defined on a finite Markov chain. Proc. Camb. Philos. Soc. 58, 286-298.
39. Mogul’skii, A. A. (1974). Factorization identities for processes with independent increments given on a Markov chain. Th. Probab. Math. Statist. 11.
40. Neuts, M. F. (1981). Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore.
41. Neuts, M. F. (1989). Structured stochastic matrices of the M/G/1 type and their applications. Marcel Delcker, New York.
42. Ney, P. & Nummelin, E. (1986). Markov additive processes. 1. Eigenvalues and limit theorems. II. Large deviations. Ann. Probab. 15, 561-592, 593-609.
43. Newbould, M. (1973). A classification of a random walk defined on a finite Markov chain. Z. Wahrscheinlichkeitsth. verw. Geb. 26, 95-104.
44. Odoni, A. R. & Roth, E. (1983). An empirical investigation of the transient behavior of stationary queuing systems. Opns. Res. 31, 432-455.
45. Presman, E. L. (1967). A boundary value problem for sums of lattice random variables given on a finite regular Markov chain. Th. Probab. Appl. 12, 323-328.
46. Presman, E. L. (1969). Factorization methods and boundary problems for sums of random variables given on a Markov chain. Math. USSR Izv. 3, 815-852 (English translation).
47. Reinhard, J. M. (1982). Identités du type Baxter-Spitzer type pour une classe de promenades aleatoires semi-Markoviennes. Ann. Inst. H. Poincaré, B, 18, 319-333.
48. Reinhard, J. M. (1984). On a class of semi-Markov risk models obtained as classical risk models in a Markovian environment. Astin Bull. 14, 23-43.
49. Regterschot, G. J. K. & de Smit, J. H. A. (1986). The queue M/G/1 with Markov-modulated arrivals and services. Math. Opns Res. 11, 465-483.
50. Seal, H. L. (1974). The numerical calculation of U(w, t), the probability of non-ruin in any interval (0, t). Scand. Actuarial J., 121-139.
51. Segerdahl, C.-O. (1955). When does ruin occur in the collective theory of risk? Skand. Aktuar. Tidsskr., 22-36.
52. Siegmund, D. (1979). Corrected diffusion approximations in certain random walk problems. Adv. Appl. Probab. 11, 701-719.
53. de Smit, J. H. A. (1986). The single server semi-Markov queue. Stoch. Proc. Appl. 22, 37-50.
54. de Smit, J. H. A. & Regterschot, G. J. K. (1986). A semi-Markov queue with exponential service time. Semi-Markov processes. Theory and applications (ed. J. Janssen), pp. 369-382. Plenum, New York.
55. Thorin, O. & Wikstad, N. (1976). Calculation of ruin probabilities when the claim distribution is lognormal. Scand. Act. J., 231-246.
56. Tweedie, M. C. K. (1960). Generalization of Wald’s fundamental identity of sequential analysis to Markov chains. Proc. Camb. Philos. Soc. 56, 205-214.
57. Volkov, I. S. (1958). On the distribution of sums of random variables defined on a homogeneous Markov chain. Th. Probab. Appl. 3.