2021/07/27 by Aldo Taranto, Taranto, Aldo, Ron Addie +3
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Complex Systems and Time Series Analysis #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #stat.AP #stat.CO #stat.TH
paper · pdf · doi:10.48550/arxiv.2107.12554
Manuscript accepted for publication in the Journal of Applied Probability & Statistics and will appear in issue 1 of volume 17 to be published in April 2022
arxiv created 2021/07/27 · openalex publication_date 2021/07/27 · arxiv updated 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSPs) constrain the random movement toward the origin steadily more and more, the further they deviate from the origin, rather than all at once imposing reflective barriers, as does the well-established theory of Ito diffusions with such reflective barriers. We identify that BGCSPs are a variant rather than a special case of the multi-skew Brownian motion (M-SBM). This is because they have their own complexities, such as the barriers being hidden (not known in advance) and not necessarily constant over time. We provide an M-SBM theoretical framework and also a simulation framework to elaborate deeper properties of BGCSPs. The simulation framework is then applied by generating numerous simulations of the constrained paths and the results are analysed. BGCSPs have applications in finance and indeed many other fields requiring graduated constraining, from both above and below the initial position.