Multiobjective Investment Policy for a Nonlinear Stochastic Financial System: A Fuzzy Approach

• Published in: IEEE transactions on fuzzy systems 2017-04, Vol.25 (2), p.460-474
• Main Authors: Wu, Chien-Feng, Chen, Bor-Sen, Zhang, Weihai
• Format: Article
• Language: English
• Subjects: Indexes; Investment; Linear-matrix-inequality (LMI)-constrained multiobjective evolution algorithm (MOEA); Mathematical model; multiobjective <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> H_{2}/H_{\infty } </tex-math> </inline-formula> </named-content> fuzzy investment policy; nonlinear stochastic jump diffusion system; Pareto optimality; Pareto optimization; Robustness; stochastic financial system; Stochastic processes; Takagi–Sugeno (T–S) fuzzy model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2016.2574926

The financial market always suffers from continuous and discontinuous (jump) changes and can be regarded as a nonlinear stochastic jump diffusion system. Most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem (MOP). In this study, a multiobjective H 2 /H ∞ fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in Pareto optimal sense, simultaneously. The Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective H 2 /H ∞ investment policy design procedure. By the help of the T-S fuzzy model, the multiobjective H 2 /H ∞ fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear-matrix-inequality-constrained (LMI-constrained) MOP to avoid solving the annoying Hamilton-Jacobi inequalities. Because the LMI-constrained MOP is not easy to directly calculate its Pareto optimal solutions, an indirect method is proposed to solve this MOP for the multiobjective H 2 /H ∞ fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems. An LMI-constrained multiobjective evolution algorithm (LMI-constrained MOEA) is also developed to efficiently solve the Pareto optimal solutions of the LMI-constrained MOP for the multiobjective H 2 /H 0', fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems. When the Pareto optimal regulation solutions are solved by the proposed LMI-constrained MOEA, investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his/her own preference.