  This paper stidies the first passage times to constant boundaries for
mixed-exponential jump diffusion processes. Explicit solutions of the Laplace
transforms of the distribution of the first passage times, the joint
distribution of the first passage times and undershoot (overshoot) are
obtained. As applications, we present explicit expression of the Gerber-Shiu
functions for surplus processes with two-sided jumps, present the analytical
solutions for popular path-dependent options such as lookback and barrier
options in terms of Laplace transforms and give a closed-form expression on the
price of the zero-coupon bond under a structural credit risk model with jumps.
