Binary market models with memory

2004/08/09 by Akihiko Inoue, Inoue, Akihiko, Yumiharu Nakano +3
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Primary 91B28 #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60F1 #msc:91B28 #secondary 60F1

paper · pdf · doi:10.48550/arxiv.math/0408119

13 pages

arxiv created 2004/08/09 · openalex publication_date 2004/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient conditions for the binary market to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate at which the arbitrage probability tends to zero as the number of periods goes to infinity.

Related

• Optimal long term investment model with memory
• Continuous-Time Random Walk with multi-step memory: An application to market dynamics
• A Black--Scholes Model with Long Memory
• Financial market models in discrete time beyond the concave case
• Alternative models for FX: pricing double barrier options in regime-switching Lévy models with memory