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2 Broad Categories of Methods of Estimating ULAE
- 1. Dollar Based Methods: Assumes ULAE expenditures track with loss dollars
- 2. Count Based Methods: Assumes that the same kind of transaction costs the same amount of ULAE regardless of claim size
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Steps of Classical Paid-To-Paid Ratio Method
- 1. Calculate Paid-To-Paid Ratio as (Paid ULAE / Paid Loss)
- 2. Assume 50% of ALAE occurs when claim is reported and 50% when closed
- 3. Estimate the percentage of ULAE remaining unpaid on open claims which are recorded on the company's books asa. Paid-To-Paid Ratio * (50% Case + IBNR) =
- b. Paid-To-Paid Ratio * 50% * (Total Reserve + IBNR)
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2 Implicit Assumptions of Classical Paid-To-Paid Ratio Method
- 1. Company's ULAE-to-loss relationship has achieved a steadystate
- 2. Relative volume and cost of future claims-management activity on unreported and open reported claims will be proportional to IBNR and case reserve dollars
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4 Inaccuracies of Classical Paid-To-Paid Ratio Method
- 1. Common application of classical method equates IBNR with claims not yet reported. In practice IBNR typically includes both IBNYR and IBNER
- 2. When volume of losses growing, paid-to-paid ratios will be overstated due to mismatch between ULAE and losses paid
- 3. 50/50 assumption may not describe company's application of resources to the various stages in the life cycle of its claims
- 4. Inflation can cause distortions
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Kittel's Method of Estimating ULAE
- 1. Kittle Ratio =
- a. Paid ULAE / 50% of (Paid Loss + Incurred Loss) or
- b. Paid ULAE / (Paid Loss + 50% of Case Reserve)
- 2. ULAE Reserve =
- a. Kittel Ratio * (50% Case Reserve + IBNR), or
- b. Kittel Ratio * 50% * (Total Reserve + IBNR)
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Mango-Allen Smoothing Adjustment to Kittel's Method
- 1. Used where actual historical calendar year paid losses are volatile
- 2. Adjustment replaces actual calendar period losses with "expected" losses for historical calendar periods, where expected losses are estimated by applying selected reporting and payment pattern to accident year estimated ultimate losses
- 3. Most likely needed when there is a relatively small number of widely varying claims
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Wendy Johnson's Method
- 1. Uses reporting and maintenance as the key transactions
- 2. Allows for explicit diff erential in amount of ULAE required for diff erent claim transactions
- 3. Assumes that ULAE costs are independent of claim size & nature
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3 Assumptions of Generalized Method
- 1. ULAE amounts spent opening claims are proportional to the ultimate cost of claims being reported
- 2. ULAE amounts spent maintaining claims are proportional to payments made
- 3. ULAE amounts spent closing claims are proportional to the ultimate cost of claims being closed
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Formula For Loss Basis of Generalized Method
- 1. B = (U1 * R) + (U2 * P) + (U3 * C)
- 2. B = M / W
- - U1 = % of ultimate ULAE spent opening claims
- - U2 = % of ultimate ULAE spent maintaining claims
- - U3 = % of ultimate ULAE spent closing claims
- - U1 + U2 + U3 = 100%
- - R = ultimate cost of claims that have been reported during the period T
- - C = ultimate cost of claims that have been closed during the period T
- - P = ultimate cost of claims that have been paid during the period T
- - W = Ratio of ultimate ULAE to ultimate loss
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Formula for Total ULAE Expenditures During Time Period T
- 1. B = (U1 * R * W) + (U2 * P * W) + (U3 * C * W)
- 2. B = B * W
- - U1 = % of ultimate ULAE spent opening claims
- - U2 = % of ultimate ULAE spent maintaining claims
- - U3 = % of ultimate ULAE spent closing claims
- - U1 + U2 + U3 = 100%
- - R = ultimate cost of claims that have been reported during the period T
- - C = ultimate cost of claims that have been closed during the period T
- - P = ultimate cost of claims that have been paid during the period T
- - W = Ratio of ultimate ULAE to ultimate loss
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4 Approaches To Estimate ULAE Reserve For A Group of Accident Years
- 1. Approach similar to Expected Loss Ratio: Unpaid ULAE =(W* x L) - M
- 2. Approach similar to B-F Method: Unpaid ULAE =
- a. W* x (L - B) =
- b. W* x U1 x [L - R(t)] + U2 x [L - P(t)] + U3 x [L - C(t)]
- 3. Approach similar to LDF method: Unpaid ULAE = M x (L/B - 1)
- 4. Approach using claim counts or transactions counts: Unpaid ULAE = Sum(Wi) x [(v1 x ri) + (v2 x oi) + (v3 x ci)]
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