
3 Reasons For Increased Popularity of Retro Rated Policies
 1. Policy returns premium to the insured for good loss experience
 2. Cash flow advantages since premiums are paid as losses are reported or paid
 3. Cost of insurance is harder to predict than in the past

2 Methods of Calculating PDLD Ratios
 1. Empirical Approach: use historical premium and loss development data
 2. Formula Approach: use retro rating plan parameters

Retro Premium Formula
 P_{n} = [BP + (CL_{n} * LCF)] * TM where
 1. P_{n} = Premium at n^{th} retro adjustment
 2. BP = Basic Premium
 3. LCF = Loss Conversion Factor
 4. TM = Tax Multiplier

PDLD Ratio for 1st Retro Adjustment
 1. P_{1} / L_{1} = [BP + (CL_{1} * LCF)] * TM / L_{1} or
 2. P_{1} / L_{1} = [(BP / L_{1}) * TM] + [(CL_{1} / L_{1}) * LCF * TM]
 3. Or Approximately,
 [(BP * TM) / (SP * ELR * %Loss_{1})] = [(CL_{1} / L_{1}) * LCF * TM]

PDLD Ratio for 2^{nd} Retro Adjustment
 PDLD_{2} =
 1. = (P_{2}  P_{1}) / (L_{2}  L_{1})
 2. = [(CL_{2}  CL_{1}) / (L_{2}  L_{1})] * LCF * TM

Loss Capping Ratio
 1. Definition: ratio of capped losses to uncapped losses
 2. Formula 1: CL_{1} / L_{1}
 3. Formula 2: LR * (1  χ  LER), where
 a) LR = uncapped loss ratio and
 b) χ = Table M charge at max  Table M charge at min
 4. Usually decreases as the data becomes more mature

Reasons Slope is Not 1 in Fitzgibbon's Method
 1. Some losses exceed loss limit, reducing slope
 2. In some plans, minimum premium exceeds basic premium
 3. A loss conversion factor (LCF) and a tax multiplier (TM) are applied to the incurred losses in the retro rating formula, thereby changing the slope of the line segment

Teng & Perkins Assumptions
 1. The premium responsiveness during subsequent adjustments is independent of the premium responsiveness during previous adjustments
 2. The slope of the line segment depends on the time period, not on the beginning loss ratio or the beginning retro premium ratios

3 Advantages of the PDLD Method (Feldblum)
 1. Modeled directly on retro formula, so it is easily explained
 2. Emphasis on the premiums sensitivity in the retro rating formula parallels the RBC loss sensitive contract offset in the underwriting risk charges and Part 7 of Schedule P
 3. May prove useful when changes in the retro rating plan parameters distort the indications of other methods

Reasons For a Change in The Slopes of Line Segments
 1. Change in the average basic premium ratio (i.e., Change in the yintercept)
 2. Change in premium responsiveness (i.e., Change in the slope)
 3. Change in the length of the loss reporting pattern (i.e., Change in the length of the line segment)

Advantage/Disadvantage of Using Retro Formula to Estimate PDLD Ratio
 1. Advantage: Responds to changes in retro rating parameters that are sold, whereas the PDLD ratios derived from the historic data may not be indicative of the future PDLD ratios
 2. Disadvantage: Possible source of bias is the use of average parameters for the LCF, TM, max, min, and per accident limitation

2 Facets of Underwriting Risk
 1. Written Premium Risk: risk that future premiums will prove inadequate to cover the future losses and expenses
 2. Reserving Risk: risk that the reserves held for accidents that have already occurred may prove inadequate

3 Reasons PDLD_{1} Usually Greater Than Unity
 1. Basic premium is included in the first retro premium computation
 2. Only a small portion of loss is limited by the retro max and per accident limit at this maturity
 3. Application of the loss conversion factor and tax multiplier results in more than a dollar of premium per dollar of loss

