The mean field optimal switching problem: Variational inequality approach

A zero-sum hybrid stochastic differential game with switching controls

“…When there are more than two modes, it needs to decide not only when to switch but also where to switch. As an important branch in control theory, optimal switching has been extensively investigated by means of variational inequalities (see Tang and Yong [24], Pham [21], Lv et al [18], and Li and Wu [17]) and backward stochastic differential equations (see Hamadène and Jeanblanc [13], Hu and Tang [16], Hamadène and Zhang [15], and Tao et al [25]). In addition, the game problems of optimal switching were discussed by Yong [29,30], Tang and Hou [23], Hamadène et al [14], and El Asri and Mazid [8].…”