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2 results

  • On the Stability of Recursive Formulas

  • Harry H. Panjer, Shaun Wang
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 23 / Issue 2 / November 1993
    Published online by Cambridge University Press:
    29 August 2014, pp. 227-258
    Print publication:
    November 1993
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  • Based on recurrence equation theory and relative error (rather than absolute error) analysis, the concept and criterion for the stability of a recurrence equation are clarified. A family of recursions, called congruent recursions, is proved to be strongly stable in evaluating its non-negative solutions. A type of strongly unstable recursion is identified. The recursive formula discussed by Panjer (1981) is proved to be strongly stable in evaluating the compound Poisson and the compound Negative Binomial (including Geometric) distributions. For the compound Binomial distribution, the recursion is shown to be unstable. A simple method to cope with this instability is proposed. Many other recursions are reviewed. Illustrative numerical examples are given.