Recursive calculation of time to ruin distributions

R. M R Cardoso, Alfredo D. Egidio Dos Reis

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In this paper we present a different approach on Dickson and Waters [Astin Bulletin 21 (1991) 199] and De Vylder and Goovaerts [Insurance: Mathematics and Economics 7 (1988) 1] methods to approximate time to ruin probabilities. By means of Markov chain application we focus on the direct calculation of the distribution of time to ruin, and we find that the above recursions appear to be less efficient, although giving the same approximation figures. We show some graphs of the time to ruin distribution for some examples, comparing the different shapes of the densities for different values of the initial surplus. Furthermore, we consider the presence of an upper absorbing barrier and apply the proposed recursion to find ruin probabilities in this case. © 2002 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)219-230
Number of pages12
JournalInsurance: Mathematics and Economics
Issue number2
Publication statusPublished - 2002


  • Barrier problems
  • Discrete time model
  • Finite time
  • Markov chain
  • Probability of ruin
  • Recursive calculation
  • Time to ruin


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