We consider the Lévy model of the perpetual American call and put
options with a negative discount rate under Poisson observations.
Similar to the continuous observation case as in De Donno et al.
(2020), the stopping region that characterizes the optimal stopping
time is either a half-line or an interval. The objective of this paper
is to obtain explicit expressions of the stopping and continuation
regions and the value function, focusing on spectrally positive and
negative cases. To this end, we compute the identities related to the
first Poisson arrival time to an interval via the scale function and
then apply those identities to the computation of the optimal
strategies. We also discuss the convergence of the optimal solutions
to those in the continuous observation case as the rate of observation
increases to infinity. Numerical experiments are also provided.
This talk is based on the joint work with Kazutoshi Yamazaki and José
Luis Pérez.
Meeting ID: 251 152 4038
Passcode: 276466