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Let be $(X_t, t\geq 0)$ be a L\'evy process which is the sum of a Brownianmotion with drift and a compound Poisson process. We consider the first passagetime $\tau_x$ at a fixed level $x>0$ by $(X_t, t\geq 0)$ and $K_x:=X_{\tau_x}-x$ the overshoot and $L_x:= x-X_{\tau_x^-}$ the undershoot. We firststudy the regularity of the density of the first passage time. Secondly, wecalculate the joint law of $(\tau_x, K_x, L_x).$

Joint law of the hitting time, overshoot and undershoot for a L\'evy process