Uncertain and Stochastic Financial Models With Multiple Delays

Abstract

This paper studies the autonomous uncertain and stochastic systems with multiple delays, which describe a financial system involving the interest rate, the investment demand and the price index. For the deterministic model associated to the uncertain financial system, we set the conditions for the existence of the delay parameter value for which the model displays a Hopf bifurcation. For the stochastic system, we identify the differential equations for the mean value as well as for the square mean value. The last part of the paper includes numerical simulations and conclusions.

[Retracted] Prediction and Application of Computer Simulation in Time‐Lagged Financial Risk Systems

“…In the financial system, because there are many uncertain factors, some economic phenomena cannot be comprehensively described by general differential equations. Scholars often add time-delay factors to differential equations when studying economic dynamics, and all these studies focus on a fixed point [12][13][14][15][16][17][18][19][20][21]. In practical application, the influence of time delay is often distributed in an interval, so the introduction of continuousdistributed time delay can better describe the actual economic market [22].…”

0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive

“…Reference [12] proposed an uncertain fractal-order form of system (1) and studied its chaos control via adaptive sliding mode. Reference [13] proposed an uncertain and stochastic form of system (1) with multiple delays. Reference [14] proposed a discrete form of system (1) and studied its Neimark-Sacker bifurcation.…”

PDϑ Control Strategy for a Fractional‐Order Chaotic Financial Model

“…Remark . In [4][5][6][7][13][14][15][16][17][18][19][20], the authors studied the various dynamics of integer-order financial models. They did not involve the fractional-order forms.…”

“…Also the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of involved controlled financial model is established. Considering the effect of time delay on the financial phenomena, Zhang and Zhu [15], Chen et al [16], Mircea et al [17], and Zhang [18] established different delayed financial models and analyzed their Hopf bifurcation or chaos control issue. In 2014, Zhao et al [19] investigated the the anticontrol of Hopf bifurcation and chaos control of model (1) by applying delayed washout filters.…”