  In this paper, we study the optimal capital structure model with endogenous
bankruptcy when the firm's asset value follows an exponential L\'evy process
with positive jumps. In the Leland-Toft framework \cite{LelandToft96}, we
obtain the optimal bankruptcy barrier in the classical continuous-observation
model and the periodic-observation model, recently studied by Palmowski et al.\
\cite{palmowski2019leland}. We further consider the two-stage optimization
problem of obtaining the optimal capital structure. Detailed numerical
experiments are conducted to study the sensitivity of the firm's
decision-making with respect to the observation frequency and positive jumps of
the asset value.
