B.11.Sturnick

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Author:
Exam8
ID:
166031
Filename:
B.11.Sturnick
Updated:
2012-08-14 18:39:00
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Table
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Description:
The California Table L / Discussion by Gillam
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  1. Differences btwn Tables M & L
    • Table L only contains California experience
    • Table L losses limited to per accident limit
    • Table L smoothes LR by replacing death cases w avg → small effect because <6% and already close to avg
    • Table L has no overlap btwn charge for limiting total losses & individual losses
  2. Table L charge φ*(r) components
    • diff btwn limited & unlimited losses
    • limited losses in XS of r*EULR
  3. Table L formulae
    • k = loss elimination ratio = [E - E(A*)] / E
    • E(L) / E = 1 - φ*(r) + Ψ*(r)
    • Ψ*(r) = φ*(r) + r - 1
    • I* = [φ*(r) - Ψ*(r)]E
    • E(L) = E - I*
    • R = BP + cL (T incl in B & c)
  4. Table L balanced plan
    • E(R) = P(1 - D), D = expense gradation
    • B = 1 - D - (cE / P) + (cE / P) [φ*(rG) - Ψ*(rH)]
  5. Table L balance equations
    • φ*(rH) - φ*(rG) = (P - PD - H) / cE
    • rG - rH = (G - h) / cE, E = unlimited
  6. Incremental charge for per accident limitation
    • should be between 0 and LER
    • depends on overlap btwn per acc & overall limit
    • size of overlap influenced by (1) per acc limit (2) ELR (3)(4) r
    • Δφ(r) = φ*(r) - φ(r)
    • B = 1 - D - cE/P + cE/P[φ(rG) + Δφ(rG) -  Ψ(rH) - Δφ(rH)]
  7. Table L construction
    • replace death losses by avg
    • cap at limit
    • LER based on agg experience
  8. Properties of Table L
    • as r → ∞, φ → k
    • as P → ∞, φ → k if r ≥ 1 - k or 1 - r if r < 1- k
    • as r → 0, φ → 1
    • as P → 0, φ → 1
  9. Properties of φ(r)
    • monotone decreasing function of the entry ratio
    • monotone decreasing function of premium
    • CA φ*(r) higher than countrywide due to higher loss variation
    • diff btwn table L & M much smaller than LER would imply due to overlap
    • Δφ(r) that does not vary by P results in overcharging small and undercharging large risks
  10. Table L limitations
    • can't be used for alternate loss limits
    • needs to be updated failry regularly for chg in Δφ(r), chg in aggregate loss dist due to fixed limit
    • using limited table is much more flexible
  11. Use of Lemma 1
    • E(L) = E(A) * [1 - φ*(r2) + Ψ*(r1)]
    • use when plans don't balance
    • use to determine P impact of updating EL size ranges
    • aggregate impact = weighted by cpy size
    • weight by prob of moving n grps

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