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

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  • Pantelous, Athanasios A.
  • Yang, Lin

Abstract

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.

Suggested Citation

  • Pantelous, Athanasios A. & Yang, Lin, 2014. "Robust LMI stability, stabilization and H∞ control for premium pricing models with uncertainties into a stochastic discrete-time framework," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 133-143.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:133-143
    DOI: 10.1016/j.insmatheco.2014.09.005
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    References listed on IDEAS

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    1. Zimbidis, Alexandros & Haberman, Steven, 2001. "The combined effect of delay and feedback on the insurance pricing process: a control theory approach," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 263-280, April.
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    Cited by:

    1. Yang, Lin & Pantelous, Athanasios A. & Assa, Hirbod, 2016. "Robust Stability, Stabilisation And H-Infinity Control For Premium-Reserve Models In A Markovian Regime Switching Discrete-Time Framework," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 747-778, September.

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    1. Zimbidis, Alexandros A., 2014. "Insurance pricing using H∞-control," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 685-697.
    2. Yang, Lin & Pantelous, Athanasios A. & Assa, Hirbod, 2016. "Robust Stability, Stabilisation And H-Infinity Control For Premium-Reserve Models In A Markovian Regime Switching Discrete-Time Framework," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 747-778, September.

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