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

Athanasios A. Pantelous and Lin Yang

Insurance: Mathematics and Economics, 2014, vol. 59, issue C, 133-143

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.

Keywords: Premium pricing; Stochastic discrete-time systems; Admissible uncertainties; Time-varying delays; Robust stabilization; Robust H∞ control; Linear Matrix Inequality (LMI) (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016766871400119X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:59:y:2014:i:c:p:133-143

DOI: 10.1016/j.insmatheco.2014.09.005

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().