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This paper considers the default probability of American lookback option in a mixed jump-diffusion model, where the underlying asset price has to cross two-sided predetermined strikes to activate the American lookback option. We study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price. By solving a system of coupled MJD-fBm, we obtain an explicit formula for the Laplace transform of the default time. Some numerical results are given for illustration. (C) 2019 Elsevier B.V. All rights reserved.