Some results on quadratic credibility premium using the balanced loss function

Purpose This paper generalizes the quadratic framework introduced by Le Courtois (2016) and Sumpf (2018), to obtain new credibility premiums in balanced case, i.e. under squared error loss function. More precisely, authors construct a net function where are estimated based on values of past observations parametric non-parametric approaches, this is useful for practitioner who wants explicitly take into account higher order (cross) moments data. Design/methodology/approach In actuarial field, theory an empirical model used calculate premium. One crucial tasks actuary insurance company design tariff structure that will fairly distribute burden claims among insureds. work, use weighted (WBLF, henceforth) premiums, WBLF generalized Zellner (1994) (see Gupta Berger (1994), pp. 371-390) which appears also Dey et al. (1999) Farsipour Asgharzadhe (2004). Findings The declare there no conflict interest funding information not applicable. Research limitations/implications work motivated following: premium effects such as clustering effect finding more credible precise, arranges both parts: insurer insured. Also, it easy apply approaches. addition, formulas (Poisson–gamma case) approach simple form may be find flexible many special cases. On other hand, neglects semi-parametric because rarely practitioners. Practical implications There several examples science (credibility). Originality/value paper, adjustment premiums.