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.

Martire, A.l. (2022). Volterra integral equations: An approach based on Lipschitz-continuity. APPLIED MATHEMATICS AND COMPUTATION, 435, 127496 [10.1016/j.amc.2022.127496].

Volterra integral equations: An approach based on Lipschitz-continuity

Martire, AL
2022-01-01

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 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.
Martire, A.l. (2022). Volterra integral equations: An approach based on Lipschitz-continuity. APPLIED MATHEMATICS AND COMPUTATION, 435, 127496 [10.1016/j.amc.2022.127496].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/425840
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