hardhat

Workers' compensation, retrospective and experience rating

Introduction

hardhat aims to bring workers' compensation calculations into a single Python package by converting the algorithms from the (historical) CAS Exam 8 material into code. We will start with Table M construction (since it's one of the easier papers).

Examples

Table M Construction

from hardhat import TableM
from hardhat.utils.utility_functions import load_sample

df = load_sample(key='brosius')

table_m = TableM(
    data=df, 
    experience='Actual Loss', 
    index="Risk"
)

print(table_m)

      Actual Loss  Entry Ratio
Risk                          
1           20000          0.2
2           50000          0.5
3           60000          0.6
4           70000          0.7
5           80000          0.8
6           80000          0.8
7           90000          0.9
8          100000          1.0
9          150000          1.5
10         300000          3.0

print(table_m.phi(r=1.2))

0.21000000000000002

Lee Diagram

table_m.lee_diagram().show()

Relevant Papers

Brosius, J. Eric, "Table M Construction," CAS Exam Study Note, 2002, pp. 1-14.

Teng, Michael T.S., "Pricing Workers' Compensation Large Deductible and Excess Insurance," Casualty Actuarial Society Forum, Winter 1994, pp. 413-437.

Feldblum, Sholom, "Workers' Compensation Ratemaking," CAS Exam Study Note, 1993.

Fisher, Ginda Kaplan; McTaggart, Lawrence; Petker, Jill; Pettingell, Rebecca, "Individual Risk Rating," CAS Study Note, 2019.

Gillam, William R., "Workers Compensation Experience Rating: What Every Actuary Should Know," PCAS LXXIX, 1992, pp. 215-254.

Meyers, Glenn G., "An Analysis of Retrospective Rating," PCAS LXVII, 1980, pp. 110-143.

Lee, Yoong-Sin, "The Mathematics of Excess of Loss Coverages and Retrospective Rating—A Graphical Approach," PCAS LXXV, 1988, pp. 49-77.

Gillam, William R., "Retrospective Rating: Excess Loss Factors," PCAS LXXVIII, 1991, pp. 1-40.

Cook, Charles F.; Lommele, Jan A.; Retterath, Ronald C., "Reserving Issues for Workers' Compensation," CLRS Transcripts, 1994, pp. 83-130.

Skurnick, David, "The California Table L," PCAS LXI, 1974, pp. 117-140.

Robertson, John P., "NCCI's 2007 Hazard Group Mapping," Variance 3(2), 2009, pp. 194-213.

Venter, Gary G., "Transformed Beta and Gamma Distributions and Aggregate Losses," PCAS LXX, 1983, pp. 156-193.

Experts needed!

If you happen to have experience in workers' compensation (*cough*, ahem), your participation will be greatly appreciated. This is intended to be a collaborative effort open to the general public.