Sharp approximations of ruin probabilities in the discrete time models

References

• Asmussen , S. 2000 . Ruin probabilities (reprinted 2001) , Singapore : World Scientific .
   Google Scholar
• Bowers , N. L. , Gerber , H. U. , Hickmann , J. C. , Jones , D. A. and Nesbitt , C. J. 1997 . Actuarial mathematics , 2nd ed , Schaumburg , IL : The Society of Actuaries .
   Google Scholar
• Cai , J., & Garrido , J. 1999 . Two sided bounds for ruin probabilities when the adjustment coefficient does not exist . Scandinavian Actuarial Journal , 80 – 92 .
   Google Scholar
• Cheng , S. , Gerber , H. U. and Shiu , E. S. W. 2000 . Discounted probabilities and ruin theory in the compound binomial model . Insurance: Mathematics and Economics , 26 : 239 – 250 .
   Web of Science ®Google Scholar
• Cossette , H. , Landriault , D. and Marceau , E. 2006 . Ruin probabilities in the discrete time renewal risk model . Insurance: Mathematics and Economics , 38 : 309 – 323 .
   Web of Science ®Google Scholar
• Daykin , C. D. , Pentikäinen , T. and Pesonen , M. 1994 . Practical risk theory for actuaries (reprinted 1995 (twice), 1996) , London : Chapman & Hall .
   Google Scholar
• De Vylder , F. E. 1978 . A practical solution to the problem of ultimate ruin probability . Scandinavian Actuarial Journal , 114 – 119 .
   Google Scholar
• Dickson , D. C. M. 2005 . Insurance risk and ruin , Cambridge : Cambridge University Press .
   Google Scholar
• Gajek , L. 2005 . On the deficit distribution when ruin occurs-discrete time model . Insurance: Mathematics and Economics , 36 : 13 – 24 .
   Web of Science ®Google Scholar
• Gerber , H. U. , Shiu , E. S. W. and Smith , N. 2008 . Methods for estimating the optimal dividend barrier and the probability of ruin . Insurance: Mathematics and Economics , 42 : 243 – 254 .
   Web of Science ®Google Scholar
• Grandell , J. 2000 . Simple approximations of ruin probabilities . Insurance: Mathematics and Economics , 26 : 157 – 173 .
   Web of Science ®Google Scholar
• Klugman , S. A. , Panjer , H. H. and Willmot , G. E. 1998 . Loss models. From data to decisions , New York : Wiley .
   Google Scholar
• Lefèvre , C., & Loisel , S. 2008 . On finite-time ruin probabilities for classical risk models . Scandinavian Actuarial Journal , 41 – 60 .
   Web of Science ®Google Scholar
• Liu , G. , Wang , Y. and Zhang , B. 2005 . Ruin probability in the continuous-time compound binomial model . Insurance: Mathematics and Economics , 36 : 303 – 316 .
   Web of Science ®Google Scholar
• Pitts , S. M. and Politis , K. 2008 . Approximations for the moments of ruin time in the compound Poisson model . Insurance: Mathematics and Economics , 42 : 668 – 679 .
   Web of Science ®Google Scholar
• Rolski , T. , Schmidli , H. , Schmidt , V. and Teugels , J. 1999 . Stochastic processes for insurance and finance , New York : Wiley .
   Google Scholar
• Rudź, M. (2007). Exact and approximate formulae for ruin probabilities-discrete time model. Master Thesis. Łódź: Technical University of Łódź, Faculty of Physics, Applied Mathematics and Computer Science, Institute of Mathematics (in Polish). The Best Master Thesis in Poland in the Field of Actuarial Sciences-the Polish National Insurance Prize (2008).
   Google Scholar
• Sangüesa , C. 2006 . Approximations of ruin probabilities in mixed Poisson models with lattice claim amounts . Insurance: Mathematics and Economics , 39 : 69 – 80 .
   Web of Science ®Google Scholar