On a switching control problem with làdlàg costs

Abstract This work addresses a switching control problem under which the cost associated with the changes of regimes is allowed to have discontinuities in time. Our main contribution is to show several characterizations of the optimal cost function as well as of 𝜀-optimal control policies. This paper is an extension of [S. Hamadène, H. Jasso-Fuentes and Y. A. Osorio-Agudelo, On a switching control problem with càdlàg costs, Stochastics 94 (2022), 1, 51–85] in the case of làdlàg processes.