Emergent dynamics of the first-order stochastic Cucker-Smale model and application to finance
- Authors
- Bae, Hyeong-Ohk; Ha, Seung-Yeal; Kim, Doheon; Kim, Yongsik; Lim, Hyuncheul; Yoo, Jane
- Issue Date
- Dec-2019
- Publisher
- John Wiley & Sons Inc.
- Keywords
- aggregation; collective dynamics; Cucker-Smale flocking; geometric Brownian motion; stochastic return
- Citation
- Mathematical Methods in the Applied Sciences, v.42, no.18, pp 6029 - 6048
- Pages
- 20
- Indexed
- SCIE
SCOPUS
- Journal Title
- Mathematical Methods in the Applied Sciences
- Volume
- 42
- Number
- 18
- Start Page
- 6029
- End Page
- 6048
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/114220
- DOI
- 10.1002/mma.5697
- ISSN
- 0170-4214
1099-1476
- 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. © 2019 John Wiley & Sons, Ltd.
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