Variance-minimizing quota share split
= Variance-minimizing quota share split
{title2=$\alpha^*=1/2$}
For any aggregate with positive finite <variance> $v$, <quota share reinsurance> with retained fraction $\alpha$ has total party <variance> $v(\alpha^2+(1-\alpha)^2)=v/2+2v(\alpha-1/2)^2$. Equal sharing uniquely minimizes this objective. The two party totals remain dependent; adding their individual <variances> is a different objective from the fixed <variance> of their sum.