Volterra integral equations: An approach based on Lipschitz-continuity

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 Cram E , r-Lundberg model framework, using its integro-differential representation as a starting point, we prove the ruin probability to be a Lips-chitz 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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this study, we consider a linear Volterra integral equation and propose a feasible, rapid, and accurate numerical algorithm by exploiting the Lipschitz continuity of the unique unknown solution. The application of this algorithm in risk theory is demonstrated using a Cramér-Lundberg model framework, where we prove the ruin probability to be a Lipschitz function. By employing the proposed algorithm, we evaluate the ruin probability that satisfies the associated Volterra integral equation and demonstrate the reasonable generalizability of the framework by considering a wide range of claim size distributions.