An evaluation of the methodology of the unknown claims reserve in compliance and liability and definition of a proper claim ratio in an insurance company

The present thesis performs an actuarial work that intends to understand the premiums, expenses, and claims, including the reserves considered the most important technical variables in an insurance company. The company is located in Colombia and the work will be performed in 2 branches: Compliance and Liability. The objective of the thesis has been set as to define and measure a claim ratio after remarking a lack of an indicator that describes the 3 most important technical variables altogether in the company. It has also defined to assess the current methodology that calculates the reserves for the claims occurred but currently unknown by the insurance company under the premise that there is a very low level of observed claims in the history of the company in both branches. All the methodologies defined, assessed, and performed in this thesis have been compared to other methodologies implemented in journals, research papers and articles to align the conclusions and take the best practices from actuarial works previously done. They all also considered to keep homogeneous results that was considered as a very important achievement even by other sources. A new methodology has been defined to calculate expenses related to administration, the ones used in the reserves and the ones related to claims. The new expenses level was used in 2021 and an impact of a tremendous increase in premiums was observed the same year as a reaction of the decrease in policy prices. The conclusions derived from the work was to continue with the current methodology to calculate the incurred but not reported claims reserve according to the instability seen in the Chain-Ladder methodology until more homogeneous result could be seen that yield to a higher level of credibility. Finally, among many possible claim ratios defined, a paid claim ratio has been considered. It includes the whole variables inside the premiums of the company and the most important variables inside the claims that were the claims paid and the proportional and non-proportional reinsurance effect