ABSTRACT
This chapter focuses on the https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> model reference investment strategy of nonlinear stochastic financial systems with continuous and discontinuous (jumping) random intrinsic fluctuation and external disturbance. The proposed https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> model reference investment strategy could not only eliminate the effect of continuous and discontinuous intrinsic fluctuations but also attenuate the worst-case effect of external disturbance on the desired reference tracking of a nonlinear stochastic financial system from the perspective of stochastic minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategy. Based on Itô–Lévy lemma and stochastic Nash game theory, the robust https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> model reference investment strategy of the stochastic nonlinear financial system is transformed to a nonlinear Hamilton–Jacobi–Issac inequality (HJII)-constrained optimization problem. Since it is not easy to solve the HJII-constrained optimization problem for stochastic minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Nash game in nonlinear stochastic financial systems, the global linearization technique is employed to interpolate several local linearized stochastic financial systems to approximate the nonlinear stochastic financial system so that the HJII-constrained optimization problem could be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which could be easily solved by LMI toolbox in Matlab. Finally, a robust https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> model reference investment strategy of nonlinear stochastic financial system and a macroeconomic robust https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_7.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> model reference control of the financial instability contagion due to international capital flow volatility are given to illustrate the design procedure and to confirm the performance of the proposed stochastic minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline14_8.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategy to the desired model reference control of the nonlinear stochastic financial system.
