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

Yang, Lin, Pantelous, Athanasios A ORCID: 0000-0001-5738-1471 and Assa, Hirbod (2016) ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK. ASTIN BULLETIN, 46 (3). pp. 746-777.

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Abstract

<jats:title>Abstract</jats:title><jats:p>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<jats:italic>H</jats:italic><jats:sub>∞</jats:sub>-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.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	Premium-reserve process, H-infinity control, system stability, Markovian regime switching systems, time-varying delay
Depositing User:	Symplectic Admin
Date Deposited:	05 Dec 2018 16:17
Last Modified:	19 Jan 2023 01:09
DOI:	10.1017/asb.2016.13
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029581

Available Versions of this Item

• ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK. (deposited 13 May 2016 13:34)
  • ROBUST STABILITY, STABILISATION AND H-INFINITY CONTROL FOR PREMIUM-RESERVE MODELS IN A MARKOVIAN REGIME SWITCHING DISCRETE-TIME FRAMEWORK. (deposited 05 Dec 2018 16:17) [Currently Displayed]