Adjustment-coefficient lower bound for NBUE claims
= Adjustment-coefficient lower bound for NBUE claims
{title2=$R\ge\theta/((1+\theta)\mu)$}
For <NBUE> claims in the <classical risk model>, the equilibrium claim size $Y$ is stochastically bounded by $X$. The positive exponential <tail integral formula for moments> gives $M_Y(R)\le M_X(R)$. Since $M_Y(R)=1+\theta$ and $M_X(R)=1+(1+\theta)\mu R$, rearrangement proves the displayed bound.