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Keywords:
Banach's Fixed-Point Theorem; classical risk model; continuity of ruin probability; probabilistic metric; ultimate ruin probability.
Banach's Fixed-Point Theorem; classical risk model; continuity of ruin probability; probabilistic metric; ultimate ruin probability.
Summary:
In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's Fixed-Point Theorem to calculate the ruin probability. Numerical results in this paper, guarantee a good approximation to the analytic solution of the ruin probability problem. Finally, we present numerical examples when claim sizes have distribution light and heavy-tailed.
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