Stochastic Models of underlying loss ratio of Catastrophe Insurance Derivatives fitted by Machine Learning Techniques

by M. J. Perez. A. Alegre. P. Devolver. J. Garcia. A. Berlanga. J. M. Molina.

The underlying loss ratio of catastrophe insurance derivatives (options and bonds) is the aggregate catastrophe losses reported before the end of certain period. In this work, catastrophes are classified in three categories and their variables (severity, number and evolution of the claim reporting process) are defined. From these previous definitions, the paper proposes several stochastic models of reported claim amount dynamics proportional to a claim rate function. From these models, the loss ratio behaviour could be determined by aggregation through the convolution of each single catastrophe distribution and we obtain the stochastic process which follows the underlying loss ratio. Three different models are considered each one based on a different definition of the claim rate function. A Machine Learning Technique, Evolution Strategies (ES) is applied to fit the claim rate of each model. ES search for the best value of claim rate and the volatility that minimize the error for several catastrophes. The available data used in this article comprise the claim rate for different natural disasters (floods) in Spain1. [via]

http://mfa2004.uclm.es/papers/p%C3%A9rez-mar%...

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