This talk will firstly discuss the recent result of paper
(Perez et al, 2018). They calculate the objective return function in
terms of scale functions from the existing fluctuation identities of
reflected-refracted Levy process. Then they derive the related variational
inequality and provide the sufficient condition for optimality of bail-out
strategy with restricted dividend rate. After that, an example which is
implied by the result will be illustrated with analytical solution.
Lastly, we propose a modified semi-smooth projected Newton method to
find the approximation of the solution and make the comparison.
Future work and remaining questions will be given at the end.
(This is the joint work with Professor Nathan Gibson).