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.

ILA LPM — Individual Life & Annuities — Life Product Management

SOA

Profit margin   PM=∑tvt Profitt∑tvt Premiumt\;PM=\dfrac{\sum_t v^t\,\text{Profit}_t}{\sum_t v^t\,\text{Premium}_t}

IRR solves ∑tProfitt (1+IRR)−t=0\sum_t \text{Profit}_t\,(1+IRR)^{-t}=0

Limited-fluctuation credibility (deaths)   nfull=(zα/2k)2,Z=min⁡ ⁣(1,d/nfull)\;n_{full}=\left(\dfrac{z_{\alpha/2}}{k}\right)^2,\quad Z=\min\!\left(1,\sqrt{d/n_{full}}\right)

Dynamic lapse   λ=λbase⋅min⁡ ⁣(U,max⁡(L, 1+m (rmkt−rcred)))\;\lambda=\lambda_{base}\cdot\min\!\big(U,\max(L,\,1+m\,(r_{mkt}-r_{cred})\big)\big)

Coinsurance profit share   Refund=max⁡(0, ρ (Pre−Cre−Ere))\;\text{Refund}=\max\big(0,\,\rho\,(P_{re}-C_{re}-E_{re})\big)

Traps to remember

  • Confusing profit margin (PV profits / PV premiums) with return on capital.

  • Ignoring the reinsurer's right to raise YRT rates when comparing reinsurance forms.

  • Recommending a COI increase without addressing the contractual basis and litigation risk.

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