Life Mortality Year-k Capital at Risk

Overview

This calculator isolates the Article 91 year-k positive-capital-at-risk measure for the Life Mortality Risk simplification.^[1] It starts from gross death-benefit amounts and best estimate obligations, then derives the net amounts after recoverables from reinsurance contracts and special purpose vehicles.

Input Terms

• Year-k Death Payment Gross: The gross amount payable in projection year k if the insured persons die under the contract.^[1]
• EPV Future Death Payments After Year k Gross: The gross expected present value of death-contingent amounts not covered by the year-k death payment and payable after year k in the event of immediate death.^[1]
• Year-k Best Estimate Obligations Gross: The corresponding gross best estimate obligations in projection year k.^[1]
• Year-k Death Payment Recoverables: Advanced inputs deduct recoverables from reinsurance contracts and special purpose vehicles for the year-k death payment component.^[1]
• Future Death Payments After Year k Recoverables: Advanced inputs deduct recoverables from reinsurance contracts and special purpose vehicles for future death payments after year k.^[1]
• Year-k Best Estimate Recoverables: Advanced inputs deduct recoverables from reinsurance contracts and special purpose vehicles for the year-k best estimate obligation component.^[1]

Technical Rationale

Article 91 defines CAR_k as the positive difference between net death-benefit amounts and the corresponding net best estimate obligations for projection year k.^[1] The zero floor prevents contracts or years with no adverse mortality exposure from offsetting positive capital-at-risk amounts.

The gross, reinsurance, and SPV split keeps the net Article 91 position traceable while preserving the same year-k capital-at-risk boundary before survival weighting, discounting, and summation across projection years.

Important Notes

• This is a year-level Article 91 input measure, not a standalone SCR amount.
• Reinsurance and SPV recoverables are always explicit advanced inputs so the net position remains traceable.