Effect of Zero-cost Interval in Running Cost for Stochastic Impulse Control Problems
Ryosuke Naito, Kazuhiro Yasuda
Effects of a zero-cost interval of a running cost on exercise boundaries in stochastic impulse control problems are considered. To study it, we basically use a numerical algorithm given in . However, convergences of its numerical solutions to the true solution in their algorithm under our settings here are not theoretically guaranteed, therefore we first extend their theorems related to convergences and mathematically prove it. Then using the valid algorithm, relations between the zero-cost intervals and the value function or optimal strategies are numerically studied.