A General Optimal Multiple Stopping Problem with an Application to Swing Options

In their paper, Carmona and Touzi [8 Carmona, R., and Touzi, N. 2008. Optimal multiple stopping and valuation of swing options. Mathematical Finance 18(2):239–268.[Crossref], [Web of Science ®] , [Google Scholar]] studied an optimal multiple stopping time problem in a market where the price process is continuous. In this article, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. We relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman variational inequality.