B.08.Gillam & Snader

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Author:
Exam8
ID:
166025
Filename:
B.08.Gillam & Snader
Updated:
2012-08-14 15:44:49
Tags:
experience rating split plan perryman
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Description:
Fundamentals of Individual Risk Rating, Part I
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  1. 2 categories of experience rating
    • no split plan: losses are not divided
    • split plans: divided into primary & XS. Primary reflects frequency (most weight); XS represents severity
  2. 2 categories of split plan
    • single split: only one split into primary & excess
    • multisplit: div into increments. Decr portion of each incr is  primary
  3. Basic formula for no split plan
    • M = [ZA + (1-Z)E] / E = 1 + Z [(A - E) / E], Z = E / (E + KE)
    • 0 ≤ Z ≤ 1, d/dE(Z) ≥ 0, d/dE(Z/E) < 0
    • if KE = k, M = (A + K) / (E + K)
  4. Split plans
    • (+) better reflect diff types of WC clms (small, med, large w indemn)
    • M = (1 / E) [ZpAp + (1-Zp)Ep + ZeAe + (1-Ze)Ee]
    • M = 1 + Zp [(Ap - Ep) / E] + Ze [(Ae - Ee) / E]
    • Zp = E / (E + KE), Ze = E / (E + JE)
    • M = 1 + [(Ap - Ep)/(E + KE)] + [(Ae - Ee)/(E + JE)]
  5. Perryman's Formula
    • goal: come up w a formula for M which does not include credibility constants
    • M = [Ap + WAe + (1-W)Ee + (1-W)K] / [E + (1-W)K]
  6. Credibility from revised experience rating plan
    • primary cr is greater for smaller risks
    • excess cr is slightly greater for smaller risks
    • primary cr is smaller for larger risks (capped at 91%) → no more self-rating
    • XS cred much smaller for larger risk (cap 57%)
  7. Primary value formulae
    • I = Increment or interval width
    • 1940: Ap = Σ I(1-d)i + (1-d)N(A-NI); max(Ap) = I * (1/d)
    • 1961: Ap = [A / (A + C)] (I + C)
    • 1991: Ap capped at $5K

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