# ELRF™ 2020 - A Complete Link Ratio Toolkit for Today's P&C Insurance Actuary

ELRF™ 2020 is for actuaries requiring deterministic or stochastic link ratio techniques coupled with the power of a relational database. The ELRF modeling framework formulates average link ratio methods as regression estimators and extends them. This includes Mack (volume weighted averages), and other weighted averages and extensions. The following link ratio modeling frameworks are included (over 144 methods):

• Extended Link Ratio Family (ELRF);
• Payment Per Claim Incurred (PPCI);
• Projected Case Estimates (PCE);
• Fisher-Lange (FL); and
• Bornhuetter-Ferguson and Expected Loss Ratio methods.

Bootstrap samples and bootstrap simulations can be generated for any stochastic link ratio method.

A fully featured relational databases forms a repository for all your loss development arrays and link ratio models.

### Extended Link Ratio Family (ELRF) modeling framework

The Extended Link Ratio Family (ELRF) modeling framework formulates average link ratio methods as regression estimators and extends them. This includes Mack (volume weighted averages), other weighted averages and extensions:

• Murphy (an intercept)
• A constant trend in the incrementals for each development period down the accident years
• Optimal combinations of intercepts, trends, and link ratios
• Control over variance assumptions (delta)

Standard deviations are computed analytically in all cases.

### The bootstrap technique

The Bootstrap technique in the ELRF module gives

• Distributions of reserves by accident years, calendar years, and total
• Percentiles, V@Rs and T-V@Rs
• … and more!

Distributions can be translated from the bootstrap sample mean to any mean specified by the user by accident period totals or calendar period totals. This allows the actuarial analyst to fit any link ratio model, obtain the means by accident (or calendar) period and apply the bootstrap using the Mack method residuals with a selected delta.

### Diagnostic statistics and graphs

Diagnostic statistics to test assumptions made by any ELRF model

• Residuals versus development year, accident year, calendar year, and fitted
• Y|X plots to test whether link ratios have predictive power in the presence of an intercept
• … and more!

The regression formulation of link ratios (Mack, Murphy, and other extensions), provides the framework for verifying the assumptions made by the link ratio techniques.