We study the smooth-pasting property for a class of conditional expectations with reflected Lévy process as underlying state process.A relationship between local times and regulators for the doubly reflected Lévy process is established.As applications,we derive the analytic pricing formula for a zero-coupon defaultable bond when the default intensity(resp.the stochastic loss rate)is modeled as one-sided(resp.double-sided)reflected Lévy processes.Finally,some numerical illustrations are provided.
