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

Masaaki Fukasawa, Takashi Sato and Jun Sekine

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Abstract: We study backward stochastic difference equations (BS{\Delta}E) 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 BS{\Delta}E.

Date: 2023-12
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