Fixed Point Theory and Insurance Loss Modeling

Abstract

This study focuses on the future development of an insurance company during difficult circumstances, which can be described by a stochastic process that must be effectively managed to achieve the best goals for the company. Effective risk or loss management models can bring in more revenue for the insurer and result in less conditional pay-out of claims to the insured. While insurance losses, risks, and premium calculation are important topics in the field, existing literature has not always stood the test of time due to the dynamic nature of insurance principles and practices. There is a need for a suitable loss model that can adjust loss rating to a particular experience and provide an appropriate and equitable premium. The aim of this research is to find sufficient conditions for the convergence of an algorithm towards a fixed point under typical insurance loss and actuarial circumstances, resulting in a uniquely determined solution. The study presents a unique fixed point, which the algorithm converges towards through straightforward and simplified generalised formulae and functions.