Michal Páleš
Katedra matematiky a aktuárstva
Fakulta hospodárskej informatiky
Abstract
Mathematical-statistical models are important tools for analysis of insurance risk. With Solvency II project, the risk theory becomes an important tool for the creation of insurance models. Implementation of various modelling techniques opens up wide possibilities of application procedures and methods of risk theory, mainly use of probability distribution in the individual risk model and then collective risk model in connection with the generation of insurance models to support computer technology. The aim of paper is presentation of application in R language. It can be used to calculate a probability distribution of total claim consider a compound Poisson distribution with parameter lambda and individual claim is discrete with implementing Panjer's recursion. We introduced derived relations for the number of claims and the total claims. Recursions apply for manually calculation at first and then for calculation with written program in language R. Further discuss about computational constraints that are associated with Panjer's recursion. Creating a significant and reliable actuarial model (scenario), based on a solid mathematical and statistical apparatus, can be providing a significant competitive advantage in the development of new product for insurance company. Find the exact model of the probability distribution of the total claims in different types of insurance is complex and challenging task. It is important to apply easier methods and use PC systems. We showed the application and connection Panjer's recursion and language R.
