We define, for all $x \in \mathbb{R}$, $\lambda^*(x) = \sup_{t \geqslant 0}(tx - \lambda(t))$. Let $\varepsilon > 0$ and $n_0$ as in Q35. Deduce that for $n \geqslant n_0$,
$$P\left(S_n \geqslant nam\right) \leqslant \mathrm{e}^{-n\left(\lambda^*(am) - \varepsilon\right)}.$$