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.

GH DP — Group & Health — Design & Pricing

SOA

Claim cost PMPM   =∑svcUtilisationsvc/100012,000×Unit costsvc×(1−cost share)\;=\sum_{svc}\dfrac{\text{Utilisation}_{svc}/1000}{12{,}000}\times\text{Unit cost}_{svc}\times(1-\text{cost share})

Premium   =Claims PMPM1−retention%\;=\dfrac{\text{Claims PMPM}}{1-\text{retention}\%} (or claims + fixed retention)

Deductible leveraging   trendnet=Claims1−DClaims0−D−1>trendgross\;\text{trend}_{net}=\dfrac{\text{Claims}_{1}-D}{\text{Claims}_{0}-D}-1>\text{trend}_{gross}

Experience rate   R=Z Xˉgroup+(1−Z) M,Z=min⁡ ⁣(1,n/nF)\;R=Z\,\bar X_{group}+(1-Z)\,M,\qquad Z=\min\!\left(1,\sqrt{n/n_F}\right)

Aggregate stop-loss attachment   =125%×expected claims\;=125\%\times\text{expected claims} (typical)

Completion factor IBNR   Incurred=PaidCF\;\text{Incurred}=\dfrac{\text{Paid}}{CF}

Traps to remember

  • Applying gross trend to net-of-deductible claims (ignoring leveraging).

  • Pooling large claims but forgetting to add back the pooling charge.

  • Ignoring MLR minimums when setting retention.

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