Pinto & Gogol
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XS LDF uses
 Smooth underlying factors
 Generate XS dvpmt factors beyond 99 mos
 Generate XS dvpmt factors for other retentions

Translate AY LDF to PY LDF
AY LDF(Age) = PY(Age + 6 mos)

Translate single line LDF vs subline LDFs
 Say three sublines with tail factor = 1 + a/b/c
 Compare to a single line with tail factor 1 + d
 Isolate x in (a + b + c) * x / 3 = d
 Adjusted factor for subline 1 is 1 + ax

XS Paid loss and ALAE dvpmt
Pd_{x to y} = Rpt_{x to y} * (Pd to rpt_{y}/Pd to rpt_{x})

Single Parameter Pareto to estimate XS LDF
 Model illustrates rpting pattern and chging char of size of loss
 LDF = d(x/k)^{qi  qj} where
 d = excess LDF at lower retention
 x = new retention
 k = lower retention
 q_{i/j} = single par pareto q at earlier/later age

Dvpmt factors by layer of ins
 e_{c,n} = f(c) / LDF_{c}
 LDF_{ult} = (f(c)  f(d))/(e_{c,n}  e_{d,n})
 LDF_{Basic,n} = (1  f(B)) / (1/LDF_{0,n}  f(B)/LDF_{B,n})

Accountspecific dvpmt
 Assumption: ratio of gross limit to retention are equal for both layers
 LDF = dc^{e} where
 c = x_{1}/k_{1}
 e = q_{i}  q_{j}
 d = LDF in first layer