Robust H-Infinity Control for a Premium Pricing Model With a Predefined Portfolio Strategy

In this paper, the robust H-infinity (⁠$H∞$⁠) control problem for a premium pricing process is investigated with parameters uncertainty. A previous model is modified by taking into account a predefined risky investment strategy. A robust $H∞$ control problem for the reserve process is proposed using linear matrix inequality (LMI) criteria. Attention is focused on the design of a state feedback controller such that the resulting closed-loop system is robustly stochastically stable with disturbance attenuation level $γ>0$⁠. Finally, a numerical example with colorful figures and tables based on the data from the Shanghai Stock Exchange market is provided illustrating clearly the impact of risky investment in the system. The MATLAB LMI Control toolbox is used for the numerical calculations.