The Parameter Variance Adjustment in Lognormal Linear Models for Loss Reserves: Bayesian vs. Frequentist Analysis

In lognormal linear models for loss reserve estimation, losses are assumed to be lognormally distributed, where the expectations of the logarithms of losses are assumed linear in explanatory variables. A parameter variance term appears in the exponent of the estimator for expected losses. There is disagreement regarding the sign of the term. It will be argued in this note that the sign depends on whether one adopts a Bayesian or Frequentist viewpoint. Each sign is correct within the appropriate paradigm. Other key words: reserving, loss distributions, curve fitting.