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Emergent dynamics of the first‐order stochastic Cucker‐Smale model and application to finance
Author(s) -
Bae HyeongOhk,
Ha SeungYeal,
Kim Doheon,
Kim Yongsik,
Lim Hyuncheul,
Yoo Jane
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5697
Subject(s) - geometric brownian motion , brownian motion , mathematics , continuous time stochastic process , stochastic process , stochastic modelling , asset (computer security) , statistical physics , order (exchange) , coupling (piping) , mathematical optimization , stochastic differential equation , computer science , diffusion process , finance , economics , physics , statistics , mechanical engineering , knowledge management , innovation diffusion , computer security , engineering
In this paper, we study stochastic aggregation properties of the financial model for the N ‐asset price process whose dynamics is modeled by the weakly geometric Brownian motions with stochastic drifts. For the temporal evolution of stochastic components of drift coefficients, we employ a stochastic first‐order Cucker‐Smale model with additive noises. The asset price processes are weakly interacting via the stochastic components of drift coefficients. For the aggregation estimates, we use the macro‐micro decomposition of the fluctuations around the average process and show that the fluctuations around the average value satisfies a practical aggregation estimate over a time‐independent symmetric network topology so that we can control the differences of drift coefficients by tuning the coupling strength. We provide numerical examples and compare them with our analytical results. We also discuss some financial implications of our proposed model.