How it works — Areivim UK risk model

The simple version

Three ideas, in plain terms.

You don’t need the mathematics to follow the logic. Here is the whole model in three steps — then, if you want it, every assumption is open to inspect and change.

How old are we?

From members whose birth date we hold, we learn the typical age people join at (~28). We use that to estimate everyone’s age and build a picture of how old the membership is today.

How many losses?

Every age carries a yearly statistical rate — the standard actuarial curve, tuned to the 55 losses the community has experienced since 2012, then set ~20% higher to stay conservative. Applied across the pool, it gives the estimated families affected each year.

What does it cost?

Each loss commits £40,000 per unmarried child's wedding, £40,000 for the surviving parent, plus £600/month support per child. Add it up, divide by the families, and you have a fair, transparent cost per household.

What each family pays per month — and what Areivim Plus adds

2026 · today

Standard Areivim (the base) Areivim Plus (added on top, from 2026) Areivim Plus starts · 2026

View year Slide back to 2012 or forward to 2100. The green area is Standard Areivim; the gold band stacked on top is the extra that Areivim Plus adds (it starts in 2026). Together they are the total cost per family. Every figure on this page follows the year you pick. 2026 · today

Each box shows its trend across the century — click any one for the full graph.

Advanced · the parameters

Every assumption, open to change.

These are the live inputs behind every figure on this page. Adjust any of them and the chart above and all calculations below update instantly. Defaults come straight from the membership data.

⌗ Membership & signups Real JoinDate counts from the membership export, with the 196 cancelled memberships removed — 6,921 active families. Bars are signups 2013→2026 (the 2012 founding year is left off for scale); the gold line is the true average across all years, the purple line the future-inflow assumption. fixed · real data

Total signups Every active family across all years — 6,921 (7,117 ever enrolled, less 196 cancelled).

Average / year The true average — total signups ÷ number of years (2012→2026 inclusive), founding year included.

Future signups / yr Assumed new families joining each year going forward (affects years after today). 375 ≈ the recent average. More young joiners holds the cost per family down.

Future mean age The average signup age assumed for future joiners — kept at today’s 28.1.

Age at signup · empirical

Mean age Average age of an adult when their family joins. 28.1 is the pooled mean of 2,061 applicant + spouse ages from the dated records (applicant 28.6, spouse 27.6).

Spread (± yrs) Standard deviation of signup age — 7.4 in the data. It sets how wide the joining-age range is around the mean.

◷ Mortality & children model

Gompertz α Baseline mortality level in q(age)=1−e^(−α·e^(β·age)). The central fit to the 55 real losses (2012–2025) is α=1.35e-5; we run it ≈20% higher (1.62e-5) as a deliberate conservative margin, so estimated losses and orphans sit a little above experience rather than below. Set α=0.0000135 for the exact central fit.

Gompertz β How fast risk accelerates with age. β=0.085 means the death rate roughly doubles every ~8 years (ln2÷0.085). The model’s mean age at death is ~48, against ~50 observed.

Drop from pool at age Members are removed from the modelled pool once they reach this age (cover assumed to lapse). Default 75.

Having children

Avg children per family Completed family size. Children are assumed to arrive from parent age ~22, then every ~2.4 years, each marrying at ~21; a child counts toward a payout only while born and not yet married. Validated against 220 real orphans: 6.5 children implies ~4.0 eligible per loss — matching the 3.96 observed; orphan age at loss lines up with the observed 16.6. Model’s pool-wide avg child age: —. 6.5

First child at age The parent’s age when their first child is born. The model spaces the remaining children from here, which sets how many are still unmarried at any given age. Default 22.

Years between children Average gap between births. With ~2.4 years and a marriage age of ~21, the model reproduces the observed ~4 eligible children and ~16.6 orphan age at a loss. Default 2.4.

♔ Benefit & orphan support levers

Benefit per child Committed when a parent is lost: £40,000 for each unmarried child's wedding plus £40,000 for the surviving parent. £40,000/child is confirmed by the records — 173 weddings already paid, £6.47M in total (£30k in older trusts). £40,000

Orphan monthly support · add-on

Per orphan, monthly Monthly cash support per orphaned child, on top of the wedding benefit, paid until the cutoff age. Yearly cost = orphans on support × £/mo × 12. One orphaned-at-birth child draws up to £151,200 in total. £600

Paid until age Children leave monthly support once they reach this age. Default 21. 21

Program starts Monthly support applies only to new orphans from this year onward. The roll then builds up over time as each stays on support until the cutoff. 2026

Advanced · cost per family

Estimated losses and the cost per family

For each member we read their estimated age, look up that age’s mortality, and — because both parents are covered — count a payout as triggered if either parent is lost. Summed across the pool, that gives the estimated losses, new orphans, total payout, and cost per family for the year you select.

The age of the membership

follows the year below

carrying liability (children still to marry) no current liability annual mortality by age

Estimating for year Drag to pick the year you’re estimating — the age chart above and every figure below stay in sync. Cost per family per month is simply the yearly figure ÷ 12. 2026 · today

Families in pool

—

Estimated losses / yr

—

Σ families(age) × [1−(1−q)²]

New yesomim / yr

—

children orphaned, under support age

Orphans on support

—

accumulated stock still under cutoff

Loss-per-family ratio

—

families ÷ estimated losses

Wedding payout / yr

—

new yesomim × benefit (committed)

Stipend cash / yr

—

orphans on support × £/mo × 12

Total payout / yr

—

wedding + stipend

Cost / family / yr

—

total ÷ families

Cost / family / month

—

yearly ÷ 12

Four programme-level trends across the century — each box tracks the selected year; click for the full graph.

Where the losses come from — rate by age band

Mortality is applied at each single year of age, not as one rate for the whole group. This table summarises it into bands — the older founding cohort does most of the work.

Age band	Families	Blended mortality	Est. losses/yr	% of losses

Blended mortality is the single-life rate q averaged across the families in that band; estimated losses apply the both-parents trigger 1−(1−q)².

Advanced · the century view

Does the programme hold up across a century?

The long-run question. With no reserve, “viable” means the annual cost per family stays affordable as the large founding cohort ages into its higher-risk years. A steady stream of young joiners is what holds the line down — set Future signups / yr above.

Projected cost per family, 2010 → 2100

Century · 2010–2100

Advanced · 2010 → 2100

Losses, orphans, payout and cost, year by year

Each box shows the figure for the selected year with its century trend behind it — click any one for the full graph.

Advanced · the method

Every figure, and how to check it

Each number here is one of the formulas below, summed over every single year of age in the pool — nothing is a flat rate or a fudge factor. The constants come straight from the input panels.

Signups per year. The starting point is how many families joined each year since 2012 — taken directly from the membership export.
Age at signup → date of birth. From dated records we know the typical joining age (~28). For anyone missing a date of birth we assign an estimated signup age, then DOB = signup year − signup age.
Age today. current age = signup age + years since joining. Ageing each cohort to today produces the histogram above.
Project the future. Every member ages a year, anyone past the exit age leaves, and a fresh young cohort joins — keeping a young left edge that holds the death rate down.
Losses → cost. Each age carries a Gompertz mortality; with two parents the trigger chance is 1 − (1 − q)². Sum for estimated losses, weight by unmarried children for the payout, divide by families for the cost.

Mortality, one parent q(age) = 1 − e^(−α·e^(β·age))
Payout triggered, both parents pₜ = 1 − (1 − q)²
Eligible children = born (age ≥ birth-age) and not yet married (age − birth-age < 21)
Estimated losses / yr = Σ families(age) × pₜ(age)
New yesomim / yr = Σ families(age) × pₜ(age) × children under cutoff
Wedding payout / yr = new yesomim × benefit. Stipend cash / yr = orphans on support × monthly × 12
Cost / family / yr = total ÷ families. / month = that ÷ 12

Live worked example · one family at age 45, current settings

How old is our pool — and how much should each family pay?