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Calculating the Gerber–Shiu function for Sparre Andersen process via collocation method

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  • Yu, Zan

Abstract

We develop a collocation framework for computing the Gerber–Shiu function in Sparre Andersen risk models. By discretizing it on collocation grids, the problem reduces to a well-conditioned linear algebraic system that is easy to implement. The method accommodates general claim-size distributions and requires only mild smoothness conditions. We derive convergence rates for the collocation solution and identify settings that yield higher-order accuracy. Numerical experiments across a variety of distributions and penalty functions confirm the approach’s accuracy, efficiency, and robustness.

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  • Yu, Zan, 2026. "Calculating the Gerber–Shiu function for Sparre Andersen process via collocation method," Statistics & Probability Letters, Elsevier, vol. 232(C).
    • Handle: RePEc:eee:stapro:v:232:y:2026:i:c:s0167715225002780
    DOI: 10.1016/j.spl.2025.110633
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    References listed on IDEAS

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