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

===== 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.