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

2023/12/18 by Masaaki Fukasawa, Fukasawa, Masaaki, Takashi Satō +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #General Finance (q-fin.GN) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.10883

openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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