Reserving 103 Zachary Zhu Agenda Review of basic

Reserving 103 Zachary Zhu

Agenda Review of basic terminology Review of prior methods Cape Cod method Frequency Severity methods Berquist-Sherman methods

Basic Terminology Data aggregation Losses Loss adjustment expense (LAE) IBNR/IBNER Development Factors Loss Ratio

Chain Ladder Method Chain ladder method aka loss development method Using loss experience from the past to predict future losses Common triangles Reported/paid losses Reported/closed with payment claim counts

Expected Claims Method Use an expected value of claims to determine ultimate losses Calculate a loss ratio using historical data and apply to year in question Main assumption: Year in question does not provide any useful information for calculating losses Deriving the loss ratio E. g. Assume a loss ratio of 80%, AY earned premium is $1 million. What is the estimated ultimate loss?

Bornhuetter-Ferguson Method

Cape Cod Method A variation of the BF method Fixed calculation to arrive at the expected claims portion of the BF method Essentially calculating the loss ratio using the current loss and “used up” premium Slightly more responsive than the BF method Drawbacks: calculations require exposures

Frequency - Severity Methods A series of methods that are designed to calculate ultimates for frequency and severity separately Simplest option: Use the development method for claim counts and average losses separately Option 2: Trended frequency -> Trended Severity Option 3: Project incremental closed claims -> Derive incremental paid severity -> Calculate incremental paid

Case Outstanding Method Implies a relationship between case outstanding and IBNR Great when used with report year triangles, and claims made liabilities Not too accurate for estimating pure IBNR Prone to distortions

Berquist – Sherman Methods One of the more complex adjustments to the chain ladder method Restatement of historical triangles Paid B-S method adjusts for changes in claims handling Reported B-S method adjusts for changes in case reserve adequacy Usage of diagnostic triangles to test for changes Closed to reported claims / disposal rates Average case reserve

ALAE and ULAE ALAE can be treated much like losses Or lumped together with losses ULAE A number of methods