Adjustment coefficient
= Adjustment coefficient
{title2=$R>0:\ \lambda(M_X(R)-1)=cR$}
The adjustment coefficient is a positive root of $\lambda(M_X(r)-1)=cr$ in the <classical risk model>. When the <moment-generating function> is finite at $R$, the process $\exp(R[\sum_{j=1}^{N_t}X_j-ct])$ is a <continuous-time martingale>. It yields the <Lundberg inequality> and, under the relevant tilted integrability, the <Cramér–Lundberg ruin asymptotic>.