Moments of First-Passage Places for Jump-Diffusion Processes

Let Tbe the first time that the time-homogeneous jump-diffusion process X(t) leaves the interval (a, b). The jump size is assumed to be a positive constant. We derive exact formulas for E[Xk(T)] in special cases. For the general case, an approximate analytical expression can be obtained for E[Xk(T)]. This expression is precise when the jump size is small.