Keywords
incurred-but-not-yet-reported loss amount
reported loss amount
asymptotic claim reporting rate
catastrophic loss index
geometric Brownian motion
How to Cite
Abstract
This article proposes a continuous model to determine the loss-index-trigger of Insurance-Linked Securities (ILS). To this aim, we consider that the total amount of the thus covered catastrophe results from the sum of two random variables, the reported claims amount and the reported-but-not-yet-reported claims amount. The central hypothesis
of our model assumes a temporary decrease of the latter, proportional to an exponential function that we call asymptotic reporting claims rate. We represent the dynamics of this decrease through a geometric Brownian motion, wheras the reported claims amount, numerator of the loss ratio intended to be determined, is obtained by the difference between the incurred-but-not-yet-reported claims amount and the catastrophe’s total amount.
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