B.02.Miccolis

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Author:
Exam8
ID:
162903
Filename:
B.02.Miccolis
Updated:
2012-08-14 13:34:12
Tags:
ILF xol pricing pure premium trend variance
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Description:
On the theory of increased limits and excess of loss pricing
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  1. Average Basic Limit Severity (ABLS) vs ILFs
    • ABLS = E[g(x;L)]
    • I'(k) = [1 - F(k)] / ABLS
    • F(x) → 1 as x → ∞
    • I'(k) → 0 as k → ∞
    • I(k) must approach a constant as k → ∞
    • past some large limit, there is no additional charge
    • I'(k) must decrease monotonically
  2. Using ILFs to price XS layers
    PP = E(N)(E[g(x;s)] - E[g(x;r)]) = E(N)ABLS(I(s) - I(r))
  3. ILF separate trending
    • could trend separately avg severity of ABLS and of ILF
    • however results suggest lower inflationary factor for large losses → counterintuitive
  4. Including process risk in P
    • Miccolis prefers variance
    • Premium = E(Y) + λVar(Y)
    • λ chosen judgmentally
    • Risk adj P = E[g(x;k)] + λE[g(x;k)2]
    • E[h(x;r,j)2] = E[g(x;s)2] - E[g(x;r)2] - 2jE[h(x;r,j)]
  5. Difficulties in creating a severity distribution from empirical data
    • have to consider development on any set of clms
    • data often comes from policies w different limits → bias
    • credibility of the dist at high end might be low
  6. Examples of parameter risk
    • catastrophes such as hurricanes, tornadoes, eq, ...
    • change in mix of business
    • small insurers face sampling errors
    • incorrect ratemaking data
    • claims practices
    • uw practices
    • social attitudes
    • judicial or legislative climate
  7. 2 dimensional ILF consistency test
    • Test 1: marginal premium per $1,000 should decr as limit incr
    • Test 2: for any 2 occurence limits, diff in ILF must not decr as aggregate limit incr
  8. Anti-selection
    • adverse: high limit = worse experience because of (1) insd who expect high loss buy high limits and (2) lawsuits influenced by limit
    • favorable: high limit = better experience because of (1) financially secure buy high limit because they have more assets and (2) insr is willing to insure good risks at higher limtis
    • in some case affects ILF
  9. ILFs vs coinsurance
    • if insure x%, P > x% PP
    • E[g(x;x%k)] > x%E[g(x;k)]
    • P = full value exposure units x coins % x coins factor x rate
  10. Rosenberg's consistency test
    • A1<2 = aggregate limit, O1<2 = occurence limit
    • A1 to A2 adds at least as much exposure at O2 as for O1
    • O1 to O2 adds a least as much exposure at A2 as for A1
    • for any 2 aggregate limits, diff in factors must not decrease as occurence limit grows

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