Actuarium

Formula sheets

Every formula on the syllabus, rendered natively, with the traps examiners set for each. Print one per exam and keep it by your desk.

Exam 8 β€” Advanced Ratemaking

CAS

Experience modification β€…β€ŠM=1+Z(AEβˆ’1)\;M=1+Z\left(\dfrac{A}{E}-1\right), NCCI split-plan form β€…β€ŠM=Ap+wAe+(1βˆ’w)Ee+BE+B\;M=\dfrac{A_p+wA_e+(1-w)E_e+B}{E+B}

Increased limits factor β€…β€ŠILF(L)=E[X∧L]+ALAE+riskΒ loadE[X∧B]+β‹―\;ILF(L)=\dfrac{E[X\wedge L]+\text{ALAE}+\text{risk load}}{E[X\wedge B]+\cdots}; layer cost β€…β€Š=E[X∧L2]βˆ’E[X∧L1]\;=E[X\wedge L_2]-E[X\wedge L_1]

Loss elimination ratio β€…β€ŠLER(d)=E[X∧d]E[X]\;LER(d)=\dfrac{E[X\wedge d]}{E[X]}

Retrospective premium β€…β€ŠR=[B+cL]T\;R=\left[B+cL\right]T bounded by HH and GG; β€…β€ŠB=eβˆ’(cβˆ’1)E+cI\;B=e-(c-1)E+cI where II is the net insurance charge

Table M insurance charge β€…β€ŠΟ•(r)=∫r∞(1βˆ’F(s))ds\;\phi(r)=\int_r^\infty(1-F(s))ds, savings β€…β€ŠΟˆ(r)=Ο•(r)+rβˆ’1\;\psi(r)=\phi(r)+r-1

Exposure vs experience rating for reinsurance: exposure curve G(d)G(d) gives the share of loss below a fraction dd of insured value.

Traps to remember

  • Forgetting the tax multiplier or applying it before the min/max in retrospective rating.

  • Using ILFs multiplicatively with class relativities where the reading says they interact (limit Γ— class).

  • Confusing loss cost of a layer with its share of premium when expense loads differ by layer.

  • Treating credibility ZZ in experience rating as n/(n+k)n/(n+k) without the split between primary and excess.

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