General undiscounted nonlinear optimal multiple stopping of linear diffusions with boundary classification

Abstract

This paper presents an extension of recent works by Trabelsi and Zoghlami (2012) and Trabelsi (2013), on the resolution of undiscounted optimal multiple stopping times problem for regular linear diffusion, which may be viewed as a generalisation of Swing options in the energy market. In the above papers, the underlying is thought as either an asset price or a spot interest rate, but is restricted to a closed interval whose upper bound is absorbing. A fixed absorbing upper boundary does not sound mathematically interesting. In the presence of state regulations or central bank policies, for example, the asset price or the spot interest rate may not be allowed to exceed a cap value, but then the cap value should act not as an absorbing boundary, but rather as a natural, entrance boundary. We therefore extend the above works to include all possible boundary classifications of the endpoints of the state space. As application, we propose a new class of compound options, referred as call on a swing options, in a Bessel market model.