CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

Marine Insurance: Frequency–Severity Claim Modeling and the Effect of Delay on Ruin Probability

Sandy Salomo Saruan (Department of Mathematics, Faculty of Information Technology, Batam Institute of Technology, Riau Islands, Indonesia)
Adhitya Ronnie Effendie (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta, Indonesia)
Rana Sahilah (Department of Mathematics, Faculty of Information Technology, Batam Institute of Technology, Riau Islands, Indonesia)



Article Info

Publish Date
30 Nov 2026

Abstract

Reporting dates do not identify claim payment times. We quantify a reporting-based payment-time assumption's effect on finite-horizon cash ruin in an idealized marine portfolio. The freMarine calibration comprises 1,109 positive-payment snapshot claims over 41 occurrence months, with negative-binomial monthly counts, finite-mixture severity, and empirical zero-inflated reporting lags. Refitted-bootstrap diagnostics assess distributional adequacy; conflicting severity diagnostics and rejected parametric lag fits remain explicit. Event-driven simulation couples immediate and proxy payments on the same occurrences and severities, with constant aggregate premiums and an empty initial system. For 250,000 paired paths over 60 months at initial surplus 2,000 EUR thousands, cash-ruin estimates are 0.2951/0.2363 for immediate/proxy payment. The paired difference is -0.0588 (95% conditional Monte Carlo interval [-0.0597,-0.0579]); mean outstanding payments are 718.79 EUR thousands. Nonnegative delay mechanically favors coupled cash surplus without discharging liabilities. Unobserved payment histories, opening claims, and policyholder behavior preclude claims of predictive superiority, a preferred handling policy, or regulatory capital needs.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...