Description: Reserving and ratemaking calculations are vital to how insurance companies perform financially. Current-day practices for predicting future loss ratio or pure premiums for reserving and ratemaking rates are not based on low prediction errors—mean squared error (MSE) criterion. This report provides mathematically optimal weights that lead to minimum MSE prediction errors, and the formulas are validated using retro-testing with real-world datasets. In this report, two main theorems are discussed, each addressing prediction of future loss ratio or pure premium and improving upon current practices for how rates and reserves are calculated.

Description: Presenters will address optimal new business written premium mix at the firm and state levels under varying competitive conditions. They will explore the use of mean-variance optimization to determine a company's optimal new business written premium mix for a given geographical area, predicting statewide product mixes using varying rate regulation scenarios, involving profit caps and measuring/testing a market's competitiveness for a given line of business. The scope of the ideas to be presented is international, applying to property, liability, individual and group life; individual and group health; disability and accidental insurance. Examples will be presented for general insurance in the United States

Description: A discussion of the point wise convergence of the Bayesian point estimates under conjugate priors belonging to the linear exponential families.