Statistical estimate of the proportional hazard premium of loss under random censoring

TL;DR

This paper develops a statistical method to estimate the excess-of-loss reinsurance premium under random right-censoring, establishing its asymptotic properties and validating performance with simulations.

Contribution

It introduces a new estimator for the proportional hazard reinsurance premium under censoring and proves its asymptotic normality.

Findings

Estimator is asymptotically normal under certain conditions.

Simulation results demonstrate the estimator's effectiveness.

Method provides a reliable approach for premium estimation with censored data.

Abstract

Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when the risks are randomly right-censored. The asymptotic normality of the proposed estimator is established under suitable conditions and its performance evaluated through sets of simulated data.