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ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK

Published online by Cambridge University Press:  11 May 2016

Lin Yang ,
Athanasios A. Pantelous  and
Hirbod Assa
Lin Yang
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK E-Mail: lin.yang@xjtlu.edu.cn
Athanasios A. Pantelous*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK, Institute for Risk and Uncertainty, University of Liverpool, Liverpool, UK
Hirbod Assa
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK, Institute for Risk and Uncertainty, University of Liverpool, Liverpool, UK E-Mail: assa@liverpool.ac.uk
*
E-Mail: A.Pantelous@liverpool.ac.uk
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Abstract

The premium pricing process and the medium- and long-term stability of the reserve policy under conditions of uncertainty present very challenging issues in relation to the insurance world. Over the last two decades, applications of Markovian regime switching models to finance and macroeconomics have received strong attention from researchers, and particularly market practitioners. However, relatively little research has so far been carried out in relation to insurance. This paper attempts to consider how a linear Markovian regime switching system in discrete-time could be applied to model the medium- and long-term reserves and the premiums (abbreviated here as the P-R process) for an insurer. Some recently developed techniques from linear robust control theory are applied to explore the stability, stabilisation and robust H∞-control of a P-R system, and the potential effects of abrupt structural changes in the economic fundamentals, as well as the insurer's strategy over a finite time period. Sufficient linear matrix inequality conditions are derived for solving the proposed sub-problems. Finally, a numerical example is presented to illustrate the applicability of the theoretical results.

Keywords

Premium-reserve processH-infinity controlsystem stabilityMarkovian regime switching systemstime-varying delay
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 747 - 778
Copyright
Copyright © Astin Bulletin 2016 

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