An analysis of the claim distribution for fire risk with regard to industrial sector

In the last few years an ever-increasing attention has been turned to the Solvency problem. Insurance Supervisors carried out deep analysis about it, with the aim to establish a solvency system better matched to the true risk of an insurance company and to ensure more protection to policyholders. Recent researches in the Solvency II emphasize the need to turn to a three-pillar approach, individualized by a minimum patrimonial requirement, examined following the insurance market complexity, supported by appropriate internal risk models to manage and estimate the default risks connected with Insurance Business. From this point of view an accurate assessment of the underwriting risk become very important. Therefore it is very meaningful to analyse the behaviour both of the claim number and of their amount with regard to different lines of business. A lot of studies were made: Poisson distribution and Negative Binomial distribution seem to be appropriate to approximate the claim number, while more attention is paid to determine a better estimate of the severity. As from use of classical distribution (Lognormal and Pareto), recently a tail analysis was examined closely, especially for skewed risks. In fact it is more and more clear that it is necessary to assess better the extreme values, considering the big influence they have on the Business Solvency. Under this point of view Embrechts and McNeil studies are the most important example. So it is interesting to analyze a specific line of business diffused in the Italian market: we will consider policies covering fire risk on the industrial sector. First we will investigate the behaviour of the amount of claims to test which distributions fit better the available data. Historical series concerning the last few years will make possible to understand if the results achieved are appropriate over all considered period. A particular attention will be also given to understand if the used distributions are able to fit well also the tails. A research like this enable us to estimate both the future evolution of the claim amount and the performance of the loss ratio, assessing if the collected premiums will be sufficient to fulfill their obligation to policyholders and other parties also in the years to come. Besides the management of different lines of business requires to study possible correlation and dependence between them: further dependences may increase the aggregate risk. So it may be interesting analyse the correlation between fire risk and another connected one still with regard to industrial sector. For this purpose the use of copulas tool is a good method that may allow quantifying the effect of carry on more than one insurance line of business.