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

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.