Premiums, acquisition cash flows, insurance revenue, financing effects and any loss component are rolled forward for coverage still to be provided.
The measurement map
One group, two liability building blocks.
For eligible short-duration general insurance groups, the Premium Allocation Approach (PAA) measures unexpired coverage separately from obligations for claims that have already occurred.
Expected claim and attributable expense cash flows are discounted where required, then increased by the Risk Adjustment for Non-financial Risk (RA).
PAA eligibility is an accounting assessment, not an engine output.
The insurer must document whether each group has coverage of one
year or less or whether PAA is a reasonable approximation to the
general measurement model.
Insurance revenue
Release the premium basis as service is provided.
Aktuari supports passage of time and an expected-risk release pattern. Passage of time uses covered days in the reporting period divided by total coverage days. An expected-risk pattern instead uses governed service weights and, for a subsequent period, a consistent prospective unearned-premium basis.
Coverage release = covered days in period / total coverage days
Insurance revenue = revenue premium basis × coverage release
Insurance revenue = revenue premium basis × coverage release
Motor demonstration
The reporting period runs from 1 April to 30 June 2026 within a 365-day coverage period. The engine's end-exclusive date arithmetic produces 90 covered days. All demonstration amounts are stated in Indonesian rupiah (IDR).
Coverage release = 90 / 365
Insurance revenue = IDR 12,000,000,000 × 90 / 365
= IDR 2,958,904,109.59
Insurance revenue = IDR 12,000,000,000 × 90 / 365
= IDR 2,958,904,109.59
When acquisition cash flows are deferred and amortised, Aktuari uses the passage-of-time release independently of an expected-risk revenue pattern:
Acquisition amortisation = IDR 1,200,000,000 × 90 / 365
= IDR 295,890,410.96
= IDR 295,890,410.96
Worked bridge
Liability for Remaining Coverage (LRC)
The closing balance starts with the opening Liability for Remaining Coverage (LRC), adds cash premiums, and then reflects the period's service, acquisition, financing and onerous-group movements.
Closing Liability for Remaining Coverage (LRC) =
opening Liability for Remaining Coverage (LRC) + premiums received
− acquisition cash flows paid − investment component paid
− insurance revenue + acquisition amortisation
+ Liability for Remaining Coverage (LRC) finance + loss component movement
− acquisition cash flows paid − investment component paid
− insurance revenue + acquisition amortisation
+ Liability for Remaining Coverage (LRC) finance + loss component movement
The opening balance is derived from the group's own history, not supplied: premiums received before the period, less acquisition cash flows paid, less revenue recognised to date, plus amortisation to date. No premium had been received by 1 April, so the opening position is a contract asset of IDR −2,663,013,698.63 (= −2,958,904,109.59 revenue recognised + 295,890,410.96 amortisation). The legacy carried balance of IDR 8,000,000,000 fails the opening-consistency control and is reported, not measured.
Opening Liability for Remaining Coverage (LRC), derived− IDR 2,663,013,698.63
Premiums received+ IDR 12,000,000,000.00
Acquisition cash flows paid− IDR 1,200,000,000.00
Investment component paid− IDR 0.00
Insurance revenue− IDR 2,958,904,109.59
Acquisition amortisation+ IDR 295,890,410.96
Liability for Remaining Coverage (LRC) finance+ IDR 0.00
LRC before loss componentIDR 5,473,972,602.74
Loss component movement (onerous group)+ IDR 2,276,027,397.26
Closing Liability for Remaining Coverage (LRC)IDR 7,750,000,000.00
The demonstration applies the one-year financing expedient to the premium-service timing and has no investment component. The onerosity test fires on this data (section 06), so the closing balance includes a loss component and equals the fulfilment cash flows for remaining coverage. Where the expedient is not used, Aktuari adjusts premium-service allocations using locked-in annual rates and records signed accretion for advance or arrears timing.
Claims already incurred
Liability for Incurred Claims (LIC)
Each future payment combines the expected claim amount and its attributable expense. Aktuari calculates the time from valuation date to payment date on a 365.25-day basis, linearly interpolates the annual rate between curve points, and applies annual compound discounting.
Yearsi = days from valuation to payment / 365.25
Discount factori = (1 + interpolated ratei)−Yearsi
Present value = Σ (claimi + expensei) × discount factori
Closing Liability for Incurred Claims (LIC) = present value + Risk Adjustment for Non-financial Risk (RA)
Discount factori = (1 + interpolated ratei)−Yearsi
Present value = Σ (claimi + expensei) × discount factori
Closing Liability for Incurred Claims (LIC) = present value + Risk Adjustment for Non-financial Risk (RA)
Present value of claim cash flows
IDR 5,469,656,679.574937202
+ Risk Adjustment for Non-financial Risk (RA) IDR 607,040,775.17647353
= Liability for Incurred Claims (LIC) IDR 6,076,697,454.751410732
+ Risk Adjustment for Non-financial Risk (RA) IDR 607,040,775.17647353
= Liability for Incurred Claims (LIC) IDR 6,076,697,454.751410732
Rates are interpolated by payment timing. Before the first or after the last supplied tenor, the nearest endpoint rate is used.
If the governed policy elects the expedient and every payment is within one calendar year of claim incurrence, the engine uses undiscounted claims plus expenses.
Compensation for uncertainty
Risk Adjustment for Non-financial Risk (RA)
Aktuari provides two transparent calculation methods. The chosen method, parameters, diversification treatment and confidence-level disclosure remain governed actuarial judgements.
The quantile is the inverse standard normal cumulative probability at a confidence level strictly between 50% and 100%.
Future capital is projected by year. A non-empty curve is required unless approved zero-curve evidence is explicitly supplied.
Motor demonstration
Standard deviation = IDR 900,000,000
Confidence level = 75%; normal quantile ≈ 0.67448975
Risk Adjustment for Non-financial Risk (RA) = IDR 900,000,000 × 0.67448975
= IDR 607,040,775.17647353
Confidence level = 75%; normal quantile ≈ 0.67448975
Risk Adjustment for Non-financial Risk (RA) = IDR 900,000,000 × 0.67448975
= IDR 607,040,775.17647353
This normal-distribution calculation is the reference engine's specified technique, not a claim that claims uncertainty is always normally distributed. Production use requires validation against the insurer's selected methodology and underlying risk distribution.
Onerous groups
Loss component roll-forward
Aktuari compares remaining-coverage fulfilment cash flows with the Liability for Remaining Coverage (LRC) before loss. It preserves separate service, finance, future-service and newly recognised loss movements rather than using an unexplained plug.
Opening fulfilment cash flows = remaining claims present value
+ remaining expense present value + remaining-coverage Risk Adjustment for Non-financial Risk (RA)
Allocation ratio = opening loss component / opening fulfilment cash flows
Service release = −allocation ratio × claim-and-risk-adjustment service releases
Finance movement = allocation ratio × loss-component finance input
New loss = max(0, closing fulfilment cash flows
− (Liability for Remaining Coverage (LRC) before loss + loss component after prior movements))
+ remaining expense present value + remaining-coverage Risk Adjustment for Non-financial Risk (RA)
Allocation ratio = opening loss component / opening fulfilment cash flows
Service release = −allocation ratio × claim-and-risk-adjustment service releases
Finance movement = allocation ratio × loss-component finance input
New loss = max(0, closing fulfilment cash flows
− (Liability for Remaining Coverage (LRC) before loss + loss component after prior movements))
Favourable future-service changes first reduce the existing loss component, never below zero. The closing loss component is added to the Liability for Remaining Coverage (LRC). The test is computed on every run, never asserted. In the current motor demonstration the fulfilment cash flows for remaining coverage are IDR 7,750,000,000.00 (claims 7,000,000,000 + expenses 150,000,000 + risk adjustment 600,000,000) against an LRC before loss of IDR 5,473,972,602.74 — the group is onerous and a new loss of IDR 2,276,027,397.26 is recognised in insurance service expense.
Performance presentation
Keep service and finance results separate.
Service expense includes incurred claims, current service expenses, acquisition expense or amortisation, loss-component service movement, and changes in incurred-claim estimates.
Based on the accounting-policy election, Aktuari assigns the finance amount to profit or loss or to Other Comprehensive Income (OCI).
Change in Liability for Incurred Claims (LIC) estimates =
closing Liability for Incurred Claims (LIC)
− opening Liability for Incurred Claims (LIC)
− incurred claims + paid claims − Liability for Incurred Claims (LIC) finance expense
Insurance service expense = incurred claims + current service expenses
+ acquisition service expense + loss-component service movement
+ change in LIC estimates
− incurred claims + paid claims − Liability for Incurred Claims (LIC) finance expense
Insurance service expense = incurred claims + current service expenses
+ acquisition service expense + loss-component service movement
+ change in LIC estimates
The finance presentation election controls location, not the total finance movement. Aktuari retains separate profit-or-loss and Other Comprehensive Income (OCI) outputs so the presentation can be reconciled without changing the underlying liability measurement.
Close the loop
Every result must reconcile.
A successful measurement produces journals and eight independent control residuals. A residual of zero means the calculated balance, its movement bridge and its journal representation agree.
LRC identity = calculated closing LRC − LRC roll-forward
LIC identity = calculated closing LIC − LIC roll-forward
RA reconciliation = closing LIC − (present value + risk adjustment)
Journal balance = total debits − total credits
Journal-to-liability = journal liability movement − calculated movement
OCI reconciliation = finance movement − (profit-or-loss + OCI split)
Terminal runoff = LRC before loss projected to end of coverage
Onerosity = closing LRC − fulfilment cash flows, floored at zero
Opening consistency = supplied opening LRC − derived opening LRC
LIC identity = calculated closing LIC − LIC roll-forward
RA reconciliation = closing LIC − (present value + risk adjustment)
Journal balance = total debits − total credits
Journal-to-liability = journal liability movement − calculated movement
OCI reconciliation = finance movement − (profit-or-loss + OCI split)
Terminal runoff = LRC before loss projected to end of coverage
Onerosity = closing LRC − fulfilment cash flows, floored at zero
Opening consistency = supplied opening LRC − derived opening LRC
- Liability for Remaining Coverage (LRC) movement agrees to its opening balance and period movements.
- Liability for Incurred Claims (LIC) movement agrees to incurred claims, payments, finance and estimate change.
- Total journal debits equal total journal credits.
- Journal movements for each liability agree to the corresponding actuarial closing balance.
- The LRC before loss component provably runs off to zero at the end of coverage.
- The onerosity test is recomputed at every reporting date and fires the loss component.
- Supplied opening balances are validated against balances derived from the group's own history.
- Insurance finance is fully allocated between profit or loss and Other Comprehensive Income (OCI).