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A mathematical model for volatility flocking with a regime switching mechanism in a stock market. (English) Zbl 1321.91097

Summary: We present a mathematical model for stock market volatility flocking. Our proposed model consists of geometric Brownian motions with time-varying volatilities coupled with Cucker-Smale (C-S) flocking and regime switching mechanisms. For all-to-all interactions, we assume that all assets’ volatilities are coupled to each other with a constant interaction weight, and we show that the common volatility emerges asymptotically and discuss its financial applications. We also provide several numerical simulations and compare them to existing analytical results.

MSC:

91B70 Stochastic models in economics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91C20 Clustering in the social and behavioral sciences
91G80 Financial applications of other theories
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