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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Sandy Salomo Saruan
Department of Mathematics, Faculty of Information Technology, Batam Institute of Technology, Riau Islands, Indonesia
Mathematics

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Marine Insurance: Frequency–Severity Claim Modeling and the Effect of Delay on Ruin Probability Sandy Salomo Saruan; Adhitya Ronnie Effendie; Rana Sahilah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44875

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.
Co-Authors Adhitya Ronnie Effendie Rana Sahilah