DETERMINATION OF THE LOSS RATE TRIGGER OF BONDS ON CATASTROPHES THROUGH A MODEL DETERMINISTIC CONTINUOUS RATE BASED MIXED CLAIMS DECLARATION (CONSTANT AND ASYMPTOTIC). ADJUSTMENT BY EVOLUTIONARY STRATEGIES

Abstract

This paper develops a model for calculating the loss index trigger of catastrophe bonds. The total catastrophe amount is defined as the sum of the claims reported amount and the incurred but not yet reported claims amount. The central hypothesis of the model is a decrease in the latter amount, proportional to a linearly increasing function up to a certain point in time and constant thereafter, called the mixed loss reporting rate. The suitability of this model to represent actual claims reporting is analyzed by studying the mathematical properties of the incurred but not yet reported claims amount function. Finally, the validity of the proposed model is studied by estimating its fundamental parameters using machine learning techniques, and the goodness of fit is tested for a sample of five floods occurring in different Spanish regions prone to this type of catastrophes.