# Claim Liabilities

September 22, 2018

CSOP 1120 Definitions:

Claim liabilities are the portion of insurance contract liabilities in respect of claims incurred on or before the calculation date.

CIA: Discounting 3.1

Cash Flow Associated with Claim Liabilities: The first step in deriving the actuarial present value is to estimate the cash flow associated with the claim liabilities in order to derive the present value of expected claim and claim adjustment expense payments. Expected claim payments are calculated by applying an expected payment pattern to the undiscounted unpaid claims.

## Summary

Claim Liabilities typically represent the largest and riskiest liability for insurance companies.  Correct estimations is critical for the longer term success and viability of insurance companies.  Claims occur during a coverage period, but may or may not be reported during that period.  Even when claims are reported the final cost may not be known for many years.

Companies typically estimate payment patterns for each loss year.  These can be applied to the subsequent development for unpaid claims that are 12-months old as of the year end:

 Age Months Payment Pattern 12 25% 24 50% 36 75% 48 100%

Unpaid claim liabilities would generally span many years:

 Accident Year Paid Future Unpaid 2019 Paid 2020 Paid 2021 Paid 2015 $100,000$0 $0$0 $0 2016$75,000 $25,000$25,000 $0$0 2017 $50,000$50,000 $25,000$25,000 $0 2018$25,000 $75,000$25,000 $25,000$25,000 Totals $250,000$150,000 $75,000$50,000 $25,000 We can discount these cash flows to 0 by using the mid-point of each of the above years as an approximate average loss date (close enough). First year (2019) would have$75,000 paid, second year (2020) would have $50,000 paid etc. ## Simplification The exam has periodically used a simplification by using just one loss year (new company start on Jan 1, 2018):  Accident Year Paid @ Dec 31, 2018 Unpaid @ Dec 31, 2018 Age Months 2019 Paid 2020 Paid 2021 Paid 2018$25,000 $75,000 12$25,000 $25,000$25,000

.

Incremental Payment(x) = $unpaid \times \frac{Age_{x}-Age_{12}}{100\% - Age_{12}}$

Present value = $\sum_{year=2019}^{N} (1+i)^{year-2018.5}\times paid_{year}$