The Exponential Premium Principle and Its Link to Credibility Theory

Abstract

Purpose: The main object of discussing this study is to introduce and derive a new alternative of the equivalence premium principle called the exponential premium principle in actuarial science. The research elaborates on how past-experience data can be incorporated into the calculation of premiums based on the exponential premium so that the premiums will be more precise and fair. Moreover, through the application of Bayesian tools and of risk theory, the connection between the exponential premium principle and the theory of credibility is established, leading in turn to the derivation of the exponential credibility premium.

Materials and Methods: The study begins with the establishment of the mathematical principles for the derivation of different methods of loss functions. The exponential loss function is one way of presenting the formulation of exponential premium principles, which makes it different from the classical equivalence and expectation principles. Bayesian inference provides individual experience with input into each of the pricing levels. Concepts of credibility theory have also been used to demonstrate the relation between the exponential premium and the credibility premium.

Findings: The results demonstrate that the exponential premium provides an even more flexible and theoretically justified framework for premium calculations compared to traditional ways. The derivation of the exponential credibility premium shows that it gives an appropriate balance between collective risk assessment through the collective risk premium and individual experience through the credibility premium, allowing for more personalized and fair insurance pricing. The study also makes note of the exponential principle's ability to encompass risk variations and shield insurers against financial instability.

Unique Contribution to Theory, Practice and Policy: Theoretical contribution: The study will enhance the body of knowledge on premium calculation principles by integrating Bayesian learning with credibility theory.  Practical application: The exponential credibility premium could improve risk assessment and hence enhance equity in insurance pricing. Policy Implications: The findings may be utilized by regulators and insurers to improve the process of premium-setting so that at least they reflect a balanced consideration of collective and individual risk in a more definitive way.