Quantile Credibility Models with Common Effects

Wei Wang, Limin Wen, Zhixin Yang and Quan Yuan
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Wei Wang: Department of Financial Engineering, Ningbo University, Ningbo 315211, China
Limin Wen: School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, China
Zhixin Yang: Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA
Quan Yuan: Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA

Risks, 2020, vol. 8, issue 4, 1-10

Abstract: Different from classical Bühlmann and Bühlmann Straub credibility models in which independence between different risks are assumed, this paper takes dependence between risks into consideration and extends the classical Bühlmann model by introducing a common stochastic shock element. What is more, instead of relying on complete information of historical data, we aim to derive the premium using quantile of the available data. By the method of linear regression, we manage to obtain the quantile credibility premium with common effects. Our result is the generalization of existing results in credibility theory. Both quantile credibility model proposed by Pitselis (2013) and credibility premium for models with dependence induced by common effects obtained by Wen et al. (2009) are special cases of our model. Numerical simulations are also presented to illustrate the impact of quantile credibility with common effect.

Keywords: credibility premium; quantile model; common effect (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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