Claims Development Triangle

Calculate the Indicated Incurred But Not Reported Reserve instantly.

Accident Year	12m	24m	36m	Latest Age	Ultimate	IBNR
AY1	Accident year 1 cumulative claims at 12m€	Accident year 1 cumulative claims at 24m€	Accident year 1 cumulative claims at 36m€	36m	€22 050 000	€1 050 000
AY2	Accident year 2 cumulative claims at 12m€	Accident year 2 cumulative claims at 24m€	Accident year 2 cumulative claims at 36m€	24m	€20 475 000	€3 475 000
AY3	Accident year 3 cumulative claims at 12m€	Accident year 3 cumulative claims at 24m€	Accident year 3 cumulative claims at 36m€	12m	€21 877 397	€8 877 397

Weighted 12->24 Factor

1.3973

Weighted 24->36 Factor

1.1471

CDF 12->Ultimate

1.6829

Selected Tail Factor

Latest-to-Ultimate CDF

1.2628

Projected Ultimate Claims

€64 402 397

Latest Cumulative Claims

€51 000 000

Projected Ultimate Claims

€64 402 397

Latest Cumulative Claims

€51 000 000

Latest-to-Ultimate CDF

1.2628

Indicated IBNR Reserve

€13 402 397

AY1 IBNR

€1 050 000

AY2 IBNR

€3 475 000

AY3 IBNR

€8 877 397

1Step 1

Derive weighted age-to-age development factors

f_{12,24} = \frac{\sum AY_{24m}}{\sum AY_{12m}},\qquad f_{24,36} = \frac{\sum AY_{36m}}{\sum AY_{24m}}

2Step 2

Build selected cumulative development factors to ultimate

CDF_{12} = f_{12,24} \times f_{24,36} \times Tail,\quad CDF_{24}=f_{24,36}\times Tail,\quad CDF_{36}=Tail

3Step 3

Project each accident year from the latest diagonal

Ultimate_{AY} = LatestCumulative_{AY} \times CDF_{latest}

4Step 4

Calculate indicated IBNR reserve

IBNR = \sum_{AY}\max(0,\;Ultimate_{AY} - LatestCumulative_{AY})

Understand the Claims Development Triangle

Overview

This calculator provides an atomistic claims-development triangle calculator for technical-provisions diagnostics.^[1]^[2] It derives weighted development factors, selected cumulative development factors, projected ultimate claims, and indicated IBNR from cumulative claims inputs.

Input Terms

Cumulative Claims by Accident Year and Development Age: Three accident years with cumulative values at 12, 24, and 36 months.
Tail Factor: Selected factor to project from 36 months to ultimate.

Technical Rationale

The calculator first computes weighted development factors from 12->24 and 24->36, then derives cumulative development factors from 12/24/36 months to ultimate using the selected tail factor. It projects AY-level ultimate claims from the latest selected maturity points and computes AY-level indicated IBNR as projected ultimate minus latest cumulative claims. The outputs include total latest cumulative claims, total projected ultimate claims, and total indicated IBNR.

Important Notes

Atomistic scope only: This calculator does not perform reserve-policy decisions or governance actions itself.
Input discipline: Cumulative claims should be provided consistently on a like-for-like basis across accident years.
Downstream use: The indicated IBNR output is designed to feed reserve-adequacy diagnostics.

Sources

Default values are illustrative sample inputs for navigation, training, and QA. Replace them with controlled data before using the result in capital analysis, governance, or reporting decisions.