Runge--Kutta numerical methods for ruin probabilities in classical risk model
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911713012482048 |
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| author | Kanakoudis, George Kanellopoulos, Lazaros |
| author_facet | Kanakoudis, George Kanellopoulos, Lazaros |
| contents | In this paper, we study Runge--Kutta methods for the computation of ruin probabilities in the classical risk model through the associated Volterra integro-differential equation. The proposed framework combines fourth-order one-step and two-step Runge--Kutta schemes with numerical quadrature formulas to approximate the convolution term. In particular, the convolution term is approximated using Newton--Cotes and Gaussian quadrature formulas, including Simpson's 1/3 rule and Pareto-adapted Gauss--Jacobi quadrature. An equivalent reformulation of the Volterra equation as a system of ordinary differential equations is also considered. Implementations for Gamma and Pareto claim-size distributions are developed. Numerical results are presented to illustrate the effectiveness of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21693 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Runge--Kutta numerical methods for ruin probabilities in classical risk model Kanakoudis, George Kanellopoulos, Lazaros Numerical Analysis 65L06, 65R20, 91G05, 91B30 In this paper, we study Runge--Kutta methods for the computation of ruin probabilities in the classical risk model through the associated Volterra integro-differential equation. The proposed framework combines fourth-order one-step and two-step Runge--Kutta schemes with numerical quadrature formulas to approximate the convolution term. In particular, the convolution term is approximated using Newton--Cotes and Gaussian quadrature formulas, including Simpson's 1/3 rule and Pareto-adapted Gauss--Jacobi quadrature. An equivalent reformulation of the Volterra equation as a system of ordinary differential equations is also considered. Implementations for Gamma and Pareto claim-size distributions are developed. Numerical results are presented to illustrate the effectiveness of the proposed methods. |
| title | Runge--Kutta numerical methods for ruin probabilities in classical risk model |
| topic | Numerical Analysis 65L06, 65R20, 91G05, 91B30 |
| url | https://arxiv.org/abs/2605.21693 |