Backward stochastic difference equations on lattices with application to market equilibrium analysis

Abstract We study backward stochastic difference equations (BS $\Delta$ Es) driven by a d -dimensional stochastic process on a lattice, whose increments take only $d+1$ possible values that generate the lattice. Interpreting the driving process as a d -dimensional asset price process, we provide applications to an optimal investment problem and to a market equilibrium analysis, where utility functionals are defined via BS $\Delta$ Es.