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Volterra integral equations: An approach based on Lipschitz-continuity

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  • Martire, Antonio Luciano

Abstract

In this study, we consider a linear Volterra integral equation of the second type whose unique unknown solution is known to be Lipschitz-continuous. Using this property, we derive a feasible, rapid, and accurate numerical algorithm. An application to risk theory is considered. More in detail in a CramȨr-Lundberg model framework, using its integro-differential representation as a starting point, we prove the ruin probability to be a Lipschitz function. Using the proposed algorithm, we evaluate the ruin probability that solves the associated Volterra integral equation. To show that the proposed framework can be reasonably generalized, we considered a wide range of claim size distributions.

Suggested Citation

  • Martire, Antonio Luciano, 2022. "Volterra integral equations: An approach based on Lipschitz-continuity," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005707
    DOI: 10.1016/j.amc.2022.127496
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