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 5 — Basic Techniques for Ratemaking & Estimating Claim Liabilities

CAS

Fundamental insurance equation   P=L+EL+EF+V⋅P+Q⋅P\;P=L+E_L+E_F+V\cdot P+Q\cdot P

Loss ratio indication Indicated change=Trended, developed LR+F1−V−QT−1\text{Indicated change}=\frac{\text{Trended, developed LR}+F}{1-V-Q_T}-1

Pure premium indication   Pˉ=Lˉ+EˉF1−V−QT\;\bar P=\dfrac{\bar L+\bar E_F}{1-V-Q_T}

Parallelogram on-level factor   OLF=current rate levelaverage rate level in period\;OLF=\dfrac{\text{current rate level}}{\text{average rate level in period}}

Chain ladder   C^i,∞=Ci,k∏j≥kf^j\;\hat C_{i,\infty}=C_{i,k}\prod_{j\ge k}\hat f_j, f^j=∑iCi,j+1∑iCi,j\hat f_j=\dfrac{\sum_i C_{i,j+1}}{\sum_i C_{i,j}}

Bornhuetter–Ferguson   IBNR^i=Pi⋅ELR⋅(1−1CDFi)\;\widehat{IBNR}_i=P_i\cdot ELR\cdot\left(1-\tfrac{1}{CDF_i}\right)

Cape Cod   ELR=∑iCi,k∑iPi/CDFi\;ELR=\dfrac{\sum_i C_{i,k}}{\sum_i P_i/CDF_i}

Traps to remember

  • Trending losses to the average accident date of the future policy period, not to the effective date.

  • Applying fixed expense as a ratio to premium instead of per exposure (or vice versa).

  • Forgetting the tail factor or applying an all-year average when a change in settlement rate calls for a recent average.

  • BF: using 1−1/CDF1-1/CDF on paid CDF when losses are reported (or the reverse).

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