Actuarial case explained
How does employment history or savings become retirement income?
Purpose
Decision informed
Distinguish a benefit set by rules from an annuity funded by an individual balance.
Benefits and cash flows
- 1Ley 73: benefit tied to weeks, wage, and age.
- 2Ley 97: individual balance converted into an annuity.
- 3The annuity transfers longevity risk to the provider.
Assumptions
| Assumption | Value / unit | Source and status |
|---|---|---|
| Regime | Ley 73 or Ley 97 | Sourced Enrollment date declared by the case |
| Annuity mortality | Bundled EMSSA-09 | Synthetic Synthetic table |
| Payment frequency | 1/m correction | Convention First-term Woolhouse approximation |
Method
Commutation and annuities
The annuity factor combines survival and discounting; Ley 73 follows a separate rule-based path.
Renta anual = Saldo / äₓResults and interpretation
The same balance buys a different annuity when mortality, rate, or payment frequency changes.
Applied example
Roberto and Sofia: two IMSS regimes
Roberto joined IMSS in 1990 and retires under the 1973 law: the benefit is determined by weeks of contributions and average wage, capped at 25 UMA. His daughter Sofia, enrolled in 2005, will retire under the 1997 law: her AFORE balance is converted into a life annuity.
Adjust the parameters to observe how the result changes.
Monthly pension, Ley 73
—
Monthly life annuity, Ley 97
—
Actuarial interpretation
Under defined benefit (Ley 73) the amount depends on the work history and the system bears the longevity risk. Under defined contribution (Ley 97) it depends on the accumulated balance and on the mortality table used to price the annuity. The applicable regime is determined by the enrollment date, not the retirement date.
Validation and limits
What is checked
- —Zero-interest identity: äₓ = 1 + eₓ.
- —Ley 73 cases for minimum weeks and age factors.
What it does not prove
- —Ley 97 omits survivor insurance required in a complete model.
- —Ley 73 simplifies the wage-level table.