TY - JOUR

T1 - Numerical Studies of Statistical Management Decisions in Conditions of Stochastic Chaos

AU - Мусаев, Александр Азерович

AU - Григорьев, Дмитрий Алексеевич

N1 - Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - The research presented in this article is dedicated to analyzing the acceptability of traditional techniques of statistical management decision-making in conditions of stochastic chaos. A corresponding example would be asset management at electronic capital markets. This formulation of the problem is typical for a large number of applications in which the managed object interacts with an unstable immersion environment. In particular, this issue arises in problems of managing gasdynamic and hydrodynamic turbulent flows. We highlight the features of observation series of the managed object’s state immersed in an unstable interaction environment. The fundamental difference between observation series of chaotic processes and probabilistic descriptions of traditional models is demonstrated. We also present an additive observation model with a chaotic system component and non-stationary noise which provides the most adequate characterization of the original observation series. Furthermore, we suggest a method for numerically analyzing the efficiency of conventional statistical solutions in the conditions of stochastic chaos. Based on numerical experiments, we establish that techniques of optimal statistical synthesis do not allow for making effective management decisions in the conditions of stochastic chaos. Finally, we propose several versions of compositional algorithms focused on the adaptation of statistical techniques to the non-deterministic conditions caused by the specifics of chaotic processes.

AB - The research presented in this article is dedicated to analyzing the acceptability of traditional techniques of statistical management decision-making in conditions of stochastic chaos. A corresponding example would be asset management at electronic capital markets. This formulation of the problem is typical for a large number of applications in which the managed object interacts with an unstable immersion environment. In particular, this issue arises in problems of managing gasdynamic and hydrodynamic turbulent flows. We highlight the features of observation series of the managed object’s state immersed in an unstable interaction environment. The fundamental difference between observation series of chaotic processes and probabilistic descriptions of traditional models is demonstrated. We also present an additive observation model with a chaotic system component and non-stationary noise which provides the most adequate characterization of the original observation series. Furthermore, we suggest a method for numerically analyzing the efficiency of conventional statistical solutions in the conditions of stochastic chaos. Based on numerical experiments, we establish that techniques of optimal statistical synthesis do not allow for making effective management decisions in the conditions of stochastic chaos. Finally, we propose several versions of compositional algorithms focused on the adaptation of statistical techniques to the non-deterministic conditions caused by the specifics of chaotic processes.

KW - Chaotic processes

KW - Currency market

KW - Forex risk control models

KW - Trends prediction

KW - chaotic processes

KW - currency market

KW - trends prediction

UR - http://www.scopus.com/inward/record.url?scp=85122993521&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/78b6cbf2-f0f4-3aba-94d7-8192fae54609/

U2 - 10.3390/math10020226

DO - 10.3390/math10020226

M3 - Article

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 2

M1 - 226

ER -