Multi-group asset flow equations and stability

Caginalp, Gunduz; DeSantis, Mark

doi:10.3934/dcdsb.2011.16.109

Cited by 8 publications

(18 citation statements)

References 19 publications

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“…In Sec. III C, we have proved that the equilibrium point of system (21) are asymptotically stable if conditions K1-K5 hold. Since system (40) is an example for system (21), the equilibrium point of system (40) is asymptotically stable if the same conditions hold.…”

Section: Article Scitationorg/journal/chamentioning

confidence: 86%

“…Theorem 3. The equilibrium point E eq M of system (21) in which all traders follow a pure value-based strategy while selling or buying asset 1 and a pure trend-based strategy while selling or buying asset 2 is asymptotically stable if the following Chaos ARTICLE scitation.org/journal/cha conditions hold:…”

Section: K1mentioning

confidence: 99%

“…3,19 Using the asset flow approach, Caginalp and his collaborators have derived dynamical systems of this type and used them to study the financial market dynamics and stability. [14][15][16][17][18][20][21][22][23][24][25][26][27] These early models capture the dynamics of a single asset market with a prescribed number of shares and cash supply (including additions in time) which are distributed to a homogenous group of traders randomly. The models are derived based on the assumptions of the basic conservation of cash and asset and microeconomics identities including the excess demand equation (2).…”

Section: Introductionmentioning

confidence: 99%

“…10,14,18,20,25,[28][29][30] Later models, constructed under the same assumptions, have been extended to a market system with a single asset, but multiple groups of investors. 6,21,27,31 These models were used to study the dynamics of a single asset market involving a heterogeneous group of investors who all have different strategies, motivations, and also budgets. Using these multi-group models, various phenomena arising in closed end funds have been analyzed, including the price change due to a change in the number of shares, 6 and the optimality of the constant rebalanced the portfolio strategy.…”

Section: Introductionmentioning

confidence: 99%

“…31 Stability analysis, the emergence of the periodic solutions via a Hopf bifurcation, and some other bifurcation properties of these models have also been studied by several researchers. 15,21,26 In this paper, we follow in the footsteps of these earlier models, but we focus on the price dynamics of a two-asset market. We still assume that the number of shares of each asset and the amount of cash are constant in time, but the trading strategies of each trader now depend on both stock prices, which couple their resulting dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Asset price dynamics for a two-asset market system

Bulut

Merdan

Swigon

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We present a mathematical model for a market involving two stocks which are traded within a single homogeneous group of investors who have similar motivations and strategies for trading. It is assumed that the market consists of a fixed amount of cash and stocks (additions in time are not allowed, so the system is closed) and that the trading group is affected by trend and valuation motivations while selling or buying each asset, but follows a strategy in which the buying of an asset depends on the other asset's price while the selling does not. By utilizing these assumptions and basic microeconomics principles, the mathematical model is obtained through a dynamical system approach. We analyze the stability of equilibrium points of the model and determine the conditions on parameters for stability. First, we prove that all equilibria are stable in the absence of a clear emphasis on a trendbased value for each stock. Second, for systems in which the group of traders attaches importance to the valuation of one stock and the trend of the other stock for trading, we establish conditions for stability and show with numerical examples that when instability occurs, it is exhibited by oscillations in the price of both stocks. Moreover, we argue the existence of periodic solutions through a Hopf bifurcation by choosing the momentum coefficient as a bifurcation parameter within this setting. Finally, we give examples and numerical simulations to support and extend the analytical results. One of the key conclusions for economics and finance is the existence of a cyclic behavior in the absence of exogenous factors according to the momentum coefficient. In particular, an equilibrium price that is stable becomes unstable as the trend based trading increases. Published under license by AIP Publishing. https:/ /doi.ARTICLE scitation.org/journal/cha that are routinely examined by practitioners. Stability analyses and numerical studies imply that equilibrium prices are stable if the group of investors focuses on only the fundamental values of the assets being traded. In contrast, trading that is largely affected by momentum effects leads to instabilities in the asset prices, which are characteristics of the crises of financial markets such as the high-tech bubble of 1998-2000 in the United States. Another important result is the possibility of the existence of periodic solutions that are not permitted in classical finance theory.

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Section: Article Scitationorg/journal/chamentioning

confidence: 86%

Section: K1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Asset price dynamics for a two-asset market system

Bulut

Merdan

Swigon

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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An Array of Aspects in the Feasibility of Different Concentrated Solar Power Technologies

Balo,

Sua

2024

Solar Energy Concentrators

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Bifurcation analysis of a single-group asset flow model

2016

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We study the stability and Hopf bifurcation analysis of an asset pricing model that based on the model introduced by Caginalp and Balenovich in 1999, under the assumption of a …xed amount of cash and stock in the system. First, we study stability analysis of equilibrium points. Choosing the momentum coe¢ cient as a bifurcation parameter, we also show that Hopf bifurcation occurs when the bifurcation parameter passes through a critical value. Analytical results are supported by numerical simulations. A key conclusion for economics and …nance is the existence of periodic solutions for an interval of the bifurcation parameter, which is the trend-based (or momentum) coe¢ cient.

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Multi-group asset flow equations and stability

Cited by 8 publications

References 19 publications

Asset price dynamics for a two-asset market system

Asset price dynamics for a two-asset market system

An Array of Aspects in the Feasibility of Different Concentrated Solar Power Technologies

Bifurcation analysis of a single-group asset flow model

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