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XS LDF uses
- Smooth underlying factors
- Generate XS dvpmt factors beyond 99 mos
- Generate XS dvpmt factors for other retentions
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Translate AY LDF to PY LDF
AY LDF(Age) = PY(Age + 6 mos)
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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
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XS Paid loss and ALAE dvpmt
Pdx to y = Rptx to y * (Pd to rpty/Pd to rptx)
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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
- qi/j = single par pareto q at earlier/later age
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Dvpmt factors by layer of ins
- ec,n = f(c) / LDFc
- LDFult = (f(c) - f(d))/(ec,n - ed,n)
- LDFBasic,n = (1 - f(B)) / (1/LDF0,n - f(B)/LDFB,n)
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Account-specific dvpmt
- Assumption: ratio of gross limit to retention are equal for both layers
- LDF = dce where
- c = x1/k1
- e = qi - qj
- d = LDF in first layer
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