B.1. Retrospective Rating

Card Set Information

Author:
EExam8
ID:
305267
Filename:
B.1. Retrospective Rating
Updated:
2015-09-06 16:01:59
Tags:
Retrospective Rating Lee Gillam Snader Brosius Skurnick
Folders:

Description:
Lee 2, Gillam & Snader 2, Brosius, Skurnick - Retrospective Rating
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user EExam8 on FreezingBlue Flashcards. What would you like to do?


  1. Types of premium calculation
    • Manual Premium = ∑(Payroll/100 * Manual Rate) for all class codes
    • Modified Premium = Manual Premium * Experience Mod Factor
    • Standard Premium = Modified Premium * Schedule Modification Factor
    • Guaranteed Cost Premium = SP * (1 - D); D reflects lower fixed expense for larger risks
  2. Retrospective rating theory
    • uses an insured's current loss experience in determining their current policy premium
    • charge an initial premium at start of term, then adjust based on reported loss experience
    • adjustments are made around 6 months after expiry, and every 12 months as losses develop
    • Premium = [UW Expenses & Profit excl taxes + (1 + Exp LAE/Exp Loss) * Actual Losses] * Tax
    • this is a simplification, if policies were rated as such there would be no point in insurance
  3. Retrospective rating properties
    • retro-rated policies have max and min premium (add capping charge to premium)
    • can also apply limit on impact of individual accident (other charge, consider overlap)
    • those limits are not coverage limits, but rather limits on losses used for retro rating
  4. Retrospective rating without an occurrence limit
    • R = (b + CA + PCV) * TH ≤ R ≤ G
    • b = basic premium to cover profit, net insurance charge (for having max/min), non-LAE
    • A = reported losses (w or w/o ALAE)
    • C = Loss Conversion Factor = 1 + Exp LAE / Loss or 1+ Exp ULAE / Loss & ALAE
    • T = [.2 + PLR(1 + μ)]/[.2 + PLR] * [1/(1 - 𝝉)]
    • μ = assessments, 𝝉 = premium based taxes
    • V = optional component = retro development factor to stabilize the first 3 adjustments (18/30/40 months); V ≈ exp % of loss unreported = (1 - 1/CDF) * ELR
  5. Balanced plan
    • if a retrospective plan is balanced, expected retro premium = prospective (GCP)
    • b = e - (C - 1)E[A] + CI
    • e = total expenses & profit excluding taxes
    • e - (C - 1)E[A] = expense component of the basic premium
    • I = net insurance charge for max and min premium (CI = converted net insurance charge)
  6. Net Insurance charge
    • H/G = (b + CAH/G)T, where AH/G are bound by aggregate limits
    • I = [ɸ(rG) - Ψ(rH)] * E[A] = Exp Losses above AG - Exp shortfall below AH
    • entry ratio = ratio of actual to expected loss
    • rG = AG/E[A], rH = AH/E[A]
  7. Retrospective Rating with an Occurrence Limit
    • standard table M no longer appropriate
    • the aggregate impacts Pr(hit max/min premium)
    • can use Limited Loss Table M, Table M with ICRLL adjustment, or Table L (Cali)
  8. Limited Loss Table M
    • R* = (bLLM + CA* + PCF + PCV)T
    • A* = reported limited loss; A ≠ A* + PF, but E[A] = E[A*] + PF
    • F = XS loss factor as % of Standard Prem
    • V is different with an occurrence limit, since development is impacted by the limit
    • Theoretically the correct approach, but it’s not used by NCCI (too many tables)
  9. Table M with Insurance Charge Reflecting Loss Limitation (ICRLL) adjustment
    • simulate / approximate the LL Table M by using standard Table M but changing the column used to be appropriate for a larger risk size
    • factor applied on E[A] is (1 + 0.8k) / (1 - k)
    • per occurrence reduces skewness of entry ratio distribution, similar to larger risks
    • compromises on accuracy for practicality
  10. Table L
    • R* = (bL + CA* + PCV)T
    • similar to LL Table M, but Table L combines occurrence charge with aggregate charge
    • California has different hazard groups than NCCI, and V varies by occurrence limit
  11. NCCI filing by state
    • in full rate states, NCCI files ELFs (denoted by F in formulas)
    • in loss cost states, NCCI files Excess Loss Pure Premium Factors (ELPPFs), so insurers must use their own ELR to calculate ELFs
  12. Creating Table M methods
    • if sample average ≠ expected value we can 1) use sample or 2) divide charges by ɸ(0)
    • using vertical slices: look at each (limited) loss separately; the average difference between unlimited and limited entry ratio is the premium charge
    • using horizontal slices: sum by loss layer, divided by expected losses
  13. Table M horizontal methodology
    • list all claims amounts & r in the first columns, including $0 and the values for AG and AH
    • add # risks at each entry ratio, then risks above (upward sum not including current)
    • calculate % risks above (previous column over total # risks)
    • ɸ(r) = 0 for largest value of r
    • ɸ(ri) = ɸ(ri+1) + (ri+1 - ri)(% risks above ri)
  14. Advantages of using vertical slices
    • more natural since it corresponds to the way the data is presented
    • easier to understand
    • quicker if you just need ɸ(r) for a few entry ratios
  15. Advantages of using horizontal slices
    • more efficient when calculating ɸ(r) for multiple values or r
    • less time consuming and computationally intensive when there are many risks since vertical slices require dealing with each risk individually
  16. Properties of Table M
    • let Y = A/E[A], with F(y) as the CDF of Y
    • for a given r, area below the horizontal line and above the curve is Ψ(r), and above the line below the curve is ɸ(r)
    • Ψ(r) = ɸ(r) + r - 1 (derived from rectangle below r line)
    • continuous : ɸ(r) = ∫r to ∞ (y - r)dF(y); Ψ(r) = ∫0 to r (r - y)dF(y)
  17. Properties of ɸ(r) and Ψ(r)
    • ɸ(0) = 1, ɸ(∞) = 0; ɸ’(r) = -G(r) ≤ 0
    • G(r) = 1 - F(r) and ɸ’’(r) = f(r) ≥ 0
    • Ψ(0) = 0, Ψ(∞) = ∞
    • Ψ’(r) = F(r) ≥ 0 and Ψ’’(r) = f(r) ≤ 0
  18. Table M Charges and Premium Size
    • as we take a sufficiently large sample of large risks, variance → 0 and all risks have the same amount of loss, so ɸ(r) = 1 - r if r ≤ 1, 0 if r > 1
    • as premium size → 0, ɸ(r) → 1
    • in the case where standard premium is not equal by risk, use SP as weight instead of # risks
  19. Net Insurance Charge
    • E[L]/E[A] = 1 + Ψ(rH) - ɸ(rG) → E[L] = E[A] - I
    • GCP = (e + E[A])T = (1 - D)P
    • b = e - (C - 1)E[A] + CI = (1 - D)P/T - CE[A] + CI
  20. Table M Balance Equations
    • b = e - (C - 1)E[A] + CI, where I depends on max/min premium; however max/min premium also depend on b, so we need trial and error to determine correct Table M row
    • charge difference: ɸ(rH) - ɸ(rG) = [(e + E[A])T - H]/[CE[A]T] = [(1 - D)P - H]/[CE[A]T]
    • entry difference: rG - rH = [G - H]/[CE[A]T]
    • once we have the 2 balance equations, we search for matching r and ɸ(r)
    • tip: to save time, assume each entry ratio pair changes the charge difference by 0.01
  21. Constructing a Limited Loss Table M
    • process is the same as Table M, except we use limited losses with r = A*/E[A*]
    • k = LER = 1 - E[A*]/E[A]
    • R* = (bLLM + CL* + PCF)T where L* is bounded above and below by AH and AG
    • balance equation is the same, except we use A* in the denominator
    • bLLM = e - (C - 1)E[A] + CILLM; note that E[A] remains the same
  22. Constructing a Table L
    • Table L charge includes the charge for the per occurrence limit with r = A*/E[A]
    • implicit charge for the current limit varies between 0 and k
    • ɸL(r) - ɸ(r) = ΨL(r) - Ψ(r) and ɸL(∞) = k
    • continuous: ɸ(r) = ∫r to ∞ (y - r)dF(y) + k; Ψ(r) = ∫0 to r(r - y)dF(y)
    • balance equations are the same except we use ɸL(rH) and ɸL(rG)
  23. Advantages of using Table L over NCCI approach
    • it is mathematically accurate in correcting for the overlap
    • there is no need for a separate per occurrence charge
    • is built on state data rather than countrywide so more accurate in California
  24. Disadvantages of Table L over NCCI approach
    • it can't be used for alternate loss limits since charge by limit is built in
    • it would require a very large number of tables countrywide
    • it needs regular updates for inflation, incremental charges and aggregate loss distribution
    • using countrywide data may be more credible than using statewide data
  25. Why low impact in replacing death claims with average
    • < 6% of total $ comes from death claims
    • most death losses are close to the average
  26. Expected Loss Groups Tables (4B)
    • ELG = risk size group baed on Adjusted Expected Losses
    • AEL = E[A] * State Hazard Group Differential * (1 + 0.8k)/(1 - k)
    • (1 + 0.8k)/(1 - k)  = loss group adjustment factor
    • the last portion is to approximate a Limited Loss Table M; if we have to use this factor, than we'll use the Limited Loss Table M balance equations for the Table M search
    • NCCI updates these tables for inflation, so they don't need to update the Table M curve
  27. Expense Ratio Tables (4D)
    • Type A tables used for stock companies, Type B for non-stock
    • table shows the e expense ratio as well as ELR, premium discount range, T
  28. Alaska Special Rating Values
    • Alaska has specially derived values
    • Hazard Groups Differentials are used in the formula to obtain Expected Losses
    • Alaska is a loss cost state, so ELPPFs are shown instead of ELFs

What would you like to do?

Home > Flashcards > Print Preview