On Application of Fixed Point Theorem to Insurance Loss Model

Abstract

The future development when an insurance company is in a difficult circumstance can be described by a stochastic process which the insurance company is tasked to manage effectively in order to achieve best goal of the company. Application of an effective risk or loss management model in an insurance company brings in more revenue for the insurer and less conditional pay-out of claims to the insured. Insurance losses, risks and premium calculation or pricing have been active and essential topics in insurance and actuarial literatures but most of these literatures did not only stand the test of time due to dynamic nature of insurance principles and practices in highly evolving environment but also lack the intuitive and detailed standard rating logic to adjust loss rating to a particular experience. There is a need to strike a balance in charging an appropriate and equitable premium by applying a suitable loss model that gives a sufficient uniquely determined solution that will not necessarily put an insurer or the insured in uncertain awkward business situations. Therefore, the objective of this research is to obtain sufficient conditions for convergence of algorithm towards a fixed point under typical insurance loss and actuarial circumstances to achieve a uniquely determined solution. At the end, a unique fixed point was determined and the algorithm formulated converges towards that point through straightforward and simplified generalised formulae and functions.