Robust LMI stability, stabilization and H∞ control for premium pricing models with uncertainties into a stochastic discrete-time framework

The premium pricing process and the reserve stability under uncertainty are very challenging issues in the insurance industry. In practice, a premium which is sufficient enough to cover the expected claims and to keep stable the derived reserves is always required. This paper proposes a premium pricing model for General (Non-Life) Insurance products, which implements a negative feedback mechanism for the known reserves with time-varying, bounded delays. The model is developed into a stochastic, discrete-time framework and norm-bounded parameter uncertainties have been also incorporated. Thus, the stability, the stabilization and the robust H∞ control for the reserve process are investigated using Linear Matrix Inequality (LMI) criteria. For the robust H∞ control, attention will be 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. Numerical examples and figures illustrate the main findings of the paper.