Emergent dynamics of the first-order stochastic Cucker-Smale model and application to finance

Title
Emergent dynamics of the first-order stochastic Cucker-Smale model and application to finance
Author
김도헌
Keywords
aggregation; collective dynamics; Cucker-Smale flocking; geometric Brownian motion; stochasticreturn
Issue Date
2019-07-15
Publisher
WILEY
Citation
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 42, no 18, page.
Abstract
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.
URI
https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5697https://repository.hanyang.ac.kr/handle/20.500.11754/192789
ISSN
1099-1476; 0170-4214
DOI
https://doi.org/10.1002/mma.5697
Appears in Collections:
COLLEGE OF SCIENCE AND CONVERGENCE TECHNOLOGY[E](과학기술융합대학) > ETC
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