The generalized equity and exact credibility premiums with examples
DOI:
https://doi.org/10.34115/basrv8n2-014Keywords:
conjugate priors, equity credibility, exact credibility, exponential family, optimal premiumsAbstract
We investigate a more generalized alternative to the conventional credibility premium that results from squared-error loss, namely, equitable credibility premium (Promislow and Young, 1999), based on exponential family, and we derive an accurate credibility for Bühlmann model with an example. We provide sufficient conditions for accurate credibility and expand a generalised formula for the credibility weight in specific circumstances. In this article, we expand upon the research conducted by Promislow and Young (2000) to include situations where an actuary is provided with data regarding a policyholder who has a more extensive exponential family. In the first section, we established our notation and reformulation of exact credibility for a Bühmann model. We derive the class of general equitable credibility premiums in the second section.
References
BUHLMANN, H. (1967) Experience rating and credibility, ASTIN Bulletin 4, 199-207.
DJEBAR, A. ZEGHDOUDI, H (2022) On bivariate credibility estimator with GLM theory, TWMS J. App. and Eng. Math. V.12, N.2, pp. 747-754
JEWELL. W.S. (1974b) Regularity conditions for exact credibility, ASTIN Bulletin8, 336-341.
KLUGMAN, S., PANJER, H., and WILLMOT, (2013). Loss Models: From Data to Decisions, Wiley, New York.
PROMISLOW, S.D. (1991) A n axiomatic characterization of some measures of unfairness, Journal of Economic Theory 53, 345-368.
PROMISLOW, S.D. and YOUNG, V.R. (1999) Equity and credibility, Scandinavian Actuarial Journal
