Games of singular control and stopping driven by spectrally one-sided Lévy processes
A two-person zero-sum game is considered wherein one player controls a Lévy process with an additive singular control and the other player stops the process at a stopping time. The payoff is the sum of integral costs depending on resp. the state process and the singular control till the stopping time, plus a terminal cost. For the cases where the spectral density of the Lévy process is supported in either positive or negative half line, a Nash equilibrium is shown to exist wherein the stopping time is based on a threshold rule, whereas the optimal singular control is a reflecting barrier for the controlled process. The proof uses sufficient conditions in terms of the associated variational inequalities. Some numerical examples are given.
scientific article; zbMATH DE number 6366967
scientific article