B.11.Sturnick

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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
 Author: Exam8 ID: 166031 Card Set: B.11.Sturnick Updated: 2012-08-14 22:39:00 Tags: Table Folders: Description: The California Table L / Discussion by Gillam Show Answers: