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Spatial global numerical computation of integral equations is introduced. Under the Cramér-Lundberg risk process, the equation models the ruin/survival probability. The difficult point is that the interval of integration is possibly not bounded. Based on the transformation of infinite range into a finite one, we are able to apply the Chebyshev-Gauss-Radau collocation method. Our numerical experiments show good performances. It is also numerically treated limiting behavior of the solution.

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Spatial Global Numerical Computation of the Integral Equations for the Ruin Probability

  • 会议论文

  • 发表日期：

    2025年

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  • Hiroko Soutome,
  • Takuya Ooura,
  • Naoyuki Ishimura,
  • Hitoshi Imai

摘要

Spatial global numerical computation of integral equations is introduced. Under the Cramér-Lundberg risk process, the equation models the ruin/survival probability. The difficult point is that the interval of integration is possibly not bounded. Based on the transformation of infinite range into a finite one, we are able to apply the Chebyshev-Gauss-Radau collocation method. Our numerical experiments show good performances. It is also numerically treated limiting behavior of the solution.