formula

$Ee^{\alpha X_t}&=&E\bigg(\frac{1}{R_t^{\alpha}}\bigg)\\ &=&\int_0^\infty \alpha y^{\alpha -1}P(1/R_t>y)dy \\ &\leq &1+\int_1^{\infty}\alpha y^{\alpha -1}\frac{1}{2\pi t}\frac{\pi}{y^2}dy\\ &=&1+\frac{\alpha }{2t(2-\alpha )}<\infty\quad \forall{t}\geq 1$