Editing Openai/695d4253-5060-8005-95db-586e777927f4 (section)

==== Again, the numeric inputs (annual Py,CyP_y, C_yPy,Cy and the list of claimants ≥$1M by year) are not shown, so below is the required calculation structure. ====

===== For each year yyy: =====
* Target claims threshold: Ty=0.96PyT_y = 0.96P_yTy=0.96Py
* Refund: Ry=max⁡(0, Ty−Cy)R_y=\max(0,\ T_y-C_y)Ry=max(0, Ty−Cy)
* Green profit: Πy=min⁡(Py−Cy, 0.04Py)\Pi_y=\min(P_y-C_y,\ 0.04P_y)Πy=min(Py−Cy, 0.04Py)

===== Let high-claimant annual costs be Hy,iH_{y,i}Hy,i for claimants with ≥$1M in claims. =====
* Stop-loss recoveries:

Recovy=∑imax⁡(0, Hy,i−1,000,000)\text{Recov}_y=\sum_i \max(0,\ H_{y,i}-1{,}000{,}000)Recovy=i∑max(0, Hy,i−1,000,000)
* Net claims after stop loss:

CySL=Cy−RecovyC^{\text{SL}}_y = C_y - \text{Recov}_yCySL=Cy−Recovy
* Add pool charge cost:

Pooly=0.01Py\text{Pool}_y = 0.01P_yPooly=0.01Py
* “All-in” cost used for profit sharing:

C~y=CySL+Pooly\tilde{C}_y = C^{\text{SL}}_y + \text{Pool}_yC~y=CySL+Pooly
Then apply the same profit-sharing rule (96% target unless changed):

ΠySL=min⁡(Py−C~y, 0.04Py)\Pi^{\text{SL}}_y = \min\big(P_y-\tilde{C}_y,\ 0.04P_y\big)ΠySL=min(Py−C~y, 0.04Py)
Interpretation: lowers volatility by capping severity, but reduces expected profit by the pool charge; net benefit depends on how large Recovy\text{Recov}_yRecovy is relative to 0.01Py0.01P_y0.01Py.

===== This changes the target net LR from 96% to 95%. =====
* Target claims threshold: Ty=0.95PyT_y = 0.95P_yTy=0.95Py
* Green profit under proposal becomes:

Πy5%=min⁡(Py−Cy, 0.05Py)\Pi^{5\%}_y = \min\big(P_y-C_y,\ 0.05P_y\big)Πy5%=min(Py−Cy, 0.05Py)
(If combined with stop loss, replace CyC_yCy with C~y\tilde{C}_yC~y above.)

Interpretation: improves Green’s retained upside (higher cap), reduces refund frequency/amount, better compensates for volatility and the “optionality” granted to the group.

===== Define (using target LR 96% unless changed): =====
* Excess profit available for sharing in year yyy:

EPy=max⁡(0, 0.96Py−C~y)EP_y=\max(0,\ 0.96P_y-\tilde{C}_y)EPy=max(0, 0.96Py−C~y)
* Excess loss above target in year yyy:

ELy=max⁡(0, C~y−0.96Py)EL_y=\max(0,\ \tilde{C}_y-0.96P_y)ELy=max(0, C~y−0.96Py)
Let fund balance at start of year yyy be Fy−1F_{y-1}Fy−1, with F0=0F_0=0F0=0, cap Fmax⁡=500,000F_{\max}=500{,}000Fmax=500,000.

Use fund to offset bad years first:

Uy=min⁡(Fy−1, ELy)U_y=\min(F_{y-1},\ EL_y)Uy=min(Fy−1, ELy)
Remaining excess loss borne by Green:

ELynet=ELy−UyEL^{\text{net}}_y = EL_y - U_yELynet=ELy−Uy
Then credit favorable-year share into the fund up to the cap:

Deposity=min⁡(EPy, Fmax⁡−(Fy−1−Uy))\text{Deposit}_y = \min(EP_y,\ F_{\max}- (F_{y-1}-U_y))Deposity=min(EPy, Fmax−(Fy−1−Uy))
Any excess beyond filling the fund is distributed:

Distributiony=EPy−Deposity\text{Distribution}_y = EP_y - \text{Deposit}_yDistributiony=EPy−Deposity
Fund recursion:

Fy=min⁡(Fmax⁡, Fy−1−Uy+Deposity)F_y = \min\big(F_{\max},\ F_{y-1}-U_y + \text{Deposit}_y\big)Fy=min(Fmax, Fy−1−Uy+Deposity)
Green profit each year (profit-sharing with fund):
* Green retains the target margin, less any net excess loss not covered by the fund:

Πyfund=0.04Py−ELynet\Pi^{\text{fund}}_y = 0.04P_y - EL^{\text{net}}_yΠyfund=0.04Py−ELynet
* If the policy terminates after 20X3, add the retained fund balance as additional profit:

Πfund,total=∑yΠyfund+F20X3\Pi^{\text{fund,total}} = \sum_y \Pi^{\text{fund}}_y + F_{20X3}Πfund,total=y∑Πyfund+F20X3
Interpretation: reduces refund payouts in early good years, creates a buffer against future bad years, and (because Green keeps the balance at termination) materially improves Green’s expected value—though it may be viewed as less favorable/less transparent to the customer.

===== 1. Net premium PyP_yPy and developed claims CyC_yCy for 20X1–20X3 =====
# For the stop-loss option: the list of Hy,iH_{y,i}Hy,i (annual claim totals by claimant for those ≥$1M)

If you paste those figures, I’ll compute the exact totals and show the full arithmetic.