“…As a result, BSDEs have developed rapidly, whether in their own development or in many other related fields such as financial mathematics, stochastic control, biology, the financial futures market, the theory of partial differential equations, and stochastic games. Reference can be made to Karoui et al [2], Hamadene and Lepeltial [3], Peng [4,5], Ren and Xia [6], and Luo et al [7], among others. Among the BSDEs, Pardoux and Rȃşcanu [8] considered BSDEs involving a subdifferential operator, which are also dubbed Backward Stochastic Variational Inequalities (BSVIs), and also utilized them with the Feymann-Kac formula to represent a solution of the multivalued parabolic partial differential equations (PDEs).…”