
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

Steps of Classical PaidToPaid Ratio Method
 1. Calculate PaidToPaid 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. PaidToPaid Ratio * (50% Case + IBNR) =
 b. PaidToPaid Ratio * 50% * (Total Reserve + IBNR)

2 Implicit Assumptions of Classical PaidToPaid Ratio Method
 1. Company's ULAEtoloss relationship has achieved a steadystate
 2. Relative volume and cost of future claimsmanagement activity on unreported and open reported claims will be proportional to IBNR and case reserve dollars

4 Inaccuracies of Classical PaidToPaid 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, paidtopaid 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

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)

MangoAllen 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

Wendy Johnson's Method
 1. Uses reporting and maintenance as the key transactions
 2. Allows for explicit differential in amount of ULAE required for different claim transactions
 3. Assumes that ULAE costs are independent of claim size & nature

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

Formula For Loss Basis of Generalized Method
 1. B = (U_{1} * R) + (U_{2} * P) + (U_{3} * 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
  U_{1} + U_{2} + U_{3} = 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

Formula for Total ULAE Expenditures During Time Period T
 1. B = (U_{1} * R * W) + (U_{2} * P * W) + (U_{3} * C * W)
 2. B = B * W
  U_{1} = % of ultimate ULAE spent opening claims
  U_{2} = % of ultimate ULAE spent maintaining claims
  U_{3} = % of ultimate ULAE spent closing claims
  U_{1} + U_{2} + U_{3} = 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

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 BF Method: Unpaid ULAE =
 a. W* x (L  B) =
 b. W* x U_{1} x [L  R(t)] + U_{2} x [L  P(t)] + U_{3} 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(W_{i}) x [(v_{1} x r_{i}) + (v_{2} x o_{i}) + (v_{3} x c_{i})]

