Backward stochastic difference equations on lattices with application to market equilibrium analysis
arXiv:2312.10883 · doi:10.1017/jpr.2025.10045
Abstract
We study backward stochastic difference equations (BSΔE) driven by a d-dimensional stochastic process on a lattice whose increments have only d + 1 possible values that generates the lattice. Regarding the driving process as a d dimensional asset price process, we give applications to an optimal investment problem and a market equilibrium analysis, where utility functionals are defined through BSΔE.