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Dynamic multi‐sector, multi‐instrument financial networks with futures: Modeling and computation
Author(s) -
Nagurney Anna,
Siokos Stavros
Publication year - 1999
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199903)33:2<93::aid-net2>3.0.co;2-y
Subject(s) - futures contract , variational inequality , computer science , mathematical optimization , projected dynamical system , financial networks , computation , convergence (economics) , portfolio , set (abstract data type) , discrete time and continuous time , financial modeling , finance , dynamical systems theory , algorithm , financial crisis , mathematics , economics , systemic risk , linear dynamical system , statistics , physics , random dynamical system , quantum mechanics , macroeconomics , programming language , economic growth
Abstract In this paper, we develop a dynamic model of financial behavior in the case of multiple sectors and multiple instruments in the presence of financial futures, which demonstrates the evolution of the underlying networks through time. The dynamic model is formulated as a projected dynamical system whose set of stationary points coincides with the set of solutions to a variational inequality problem. We identify the network structure of the individual sectors' portfolio optimization problems out of equilibrium and then prove that the equilibrium solution can be reformulated as the solution to a network optimization problem, in which the network represents a merger of the individual networks. We subsequently provide a discrete time algorithm for the solution of the continuous time financial model, which exploits the network structure, and provide convergence results. The model and algorithm are then illustrated through numerical examples. © 1999 John Wiley & Sons, Inc. Networks 33: 93–108, 1999