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

Sandy Salomo Saruan, Adhitya Ronnie Effendie, Rana Sahilah

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.

Keywords


Delayed claims; Marine insurance; Mixture distribution; Ruin probability.

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DOI: https://doi.org/10.18860/cauchy.v11i2.44875

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