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Original article

Estimation of the Lundberg coefficient for a Markov modulated risk model

Pages 48-57 | Received 29 Mar 1995, Published online: 22 Dec 2011

References

  • Ammeter , H. 1948 . A generalization of the collective theory of risk in regard to fluctuating basic probabilities . Skand. Aktuar Tidskr. , : 171 – 198 .
  • Asmussen , S. 1989 . Risk theory in a Markovian environment . Scand. Actuarial J. , : 66 – 100 .
  • Asmussen , S. 1994 . Ruin probabilities , Aalborg University . Book manuscript
  • Asmussen , S. and Petersen , S. S. 1989 . Ruin probabilities expressed in terms of storage processe∼ . Adv. in Appl. Probab. , 20 : 913 – 916 .
  • Björk , T. and Grandell , J. 1988 . Exponential inequalities for ruin probabilities in the Cox case . Scand. Actuarial. J. , : 77 – 111 .
  • Csörgö , M. and Steinebach , J. 1991 . On the estimation of the adjustment coefficient in risk theory via intermediate order statistics . Insurance Math. Econom. , 10 : 37 – 50 .
  • Davis , M. H. A. 1984 . Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models . J. R. Statist. Soc. B , 46 : 353 – 388 .
  • Deheuvels , P. , Haeusler , E. and Mason , D. M. 1988 . Almost sure convergence of the Hill estimator . Math. Proc. Camb. Phil. Soc. , 104 : 371 – 381 .
  • Embrechts , P. , Grandell , J. and Schmidli , H. 1993 . Finite-time Lundberg inequalities in the Cox case . Scand. Actuarial J. , : 17 – 41 .
  • Embrechts , P. and Mikosch , T. 1991 . A bootstrap procedure for estimating the adjustment coefficient . Insurance Math. Econom. , 10 : 181 – 190 .
  • Furrer , H. J. and Schmidli , H. 1994 . Exponential inequalities for ruin probabilities of risk processes perturbed by diffusion . Insurance Math. Econom. , 15 : 23 – 36 .
  • Gerber , H. U. 1973 . Martingales in risk theory . Schweiz. Verein. Versicherungsmath. Mitt. , 73 : 205 – 216 .
  • Gerber , H. U. 1979 . An introduction to mathematical risk theory , Philadelphia : Huebner Foundation Monographs .
  • Grandell , J. 1979 . Empirical bounds for ruin probabilities . Stochastic Process. Appl. , 8 : 243 – 255 .
  • Grandell , J. 1991 . Aspects of risk theory , New York : Springer-Verlag .
  • Haeusler , E. and Teugels , J. L. 1985 . On asymptotic normality of Hill's estimator for the exponent of regular variation . Ann. Statist. , 13 : 743 – 756 .
  • Hall , P. 1982 . On some simple estimates of an exponent of regular variation . J. R. Statist. Soc. B , 44 : 37 – 42 .
  • Herkenrath , U. 1986 . On the estimation of the adjustment coefficient in risk theory by means of stochastic approximation procedures . Insurance Math. Econom. , 5 : 305 – 313 .
  • Hill , B. M. 1975 . A simple general approach to interference about the tail of a distribution . Ann. Statist. , 3 : 1163 – 1174 .
  • Pitts , S. M. , Grübel , R. and Embrechts , P. 1995 . Confidence bounds for the adjustment coefficient . preprint ,
  • Schmidli , H. 1996 . Lundberg inequalities for a Cox model with a piecewise constant intensity . J. Appl. Probab. , 33 to appear.
  • Smith , R. L. 1987 . Estimating tails of probability distributions . Ann. Statist. , 15 : 1174 – 1207 .

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