Let T(x) be the first time the time-homogeneous jump-diffusion process X(t), starting from X(0) = x, leaves the interval (a, b). The jump size is assumed to have an asymmetric double exponential distribution. The integro-differential equation satisfied by the moment-generating function of T(x) is transformed into an ordinary differential equation and is solved explicitly in particular cases. Explicit and exact results are also obtained for the mean of T(x) as well as the probability P[X(T(x)) ≤ a].
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