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We investigate the Levy insurance risk model with tax under Cram\'er'scondition. A direct analogue of Cram\'er's estimate for the probability of ruinin this model is obtained, together with the asymptotic distribution,conditional on ruin occurring, of several variables of interest related to ruinincluding the surplus immediately prior to ruin (undershoot) and shortfall atruin (overshoot). We also compute the present value of all tax paid conditionalon ruin occurring. The proof involves first transferring results from the modelwith no tax to the reflected process, and from there to the model with tax. Indoing so we also derive new results for the reflected process.

General tax structures for a L\'evy insurance risk process under the Cram\'er condition