B.02.Miccolis

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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
 Author: Exam8 ID: 162903 Card Set: B.02.Miccolis Updated: 2012-08-14 17:34:12 Tags: ILF xol pricing pure premium trend variance Folders: Description: On the theory of increased limits and excess of loss pricing Show Answers: