On the robust stability of pricing models for non-life insurance products
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On the robust stability of pricing models for non-life insurance products Athanasios A. Pantelous • Athanasios Papageorgiou
Received: 1 September 2011 / Accepted: 10 June 2013 / Published online: 8 October 2013 Ó DAV / DGVFM 2013
Abstract One of the most significant and challenging problems in actuarial practice, especially for general insurance, is the modelling of the premium pricing process and furthermore its stability. The classical actuarial approach to calculating the premium simply covers the expected claims, with an increase for eventual expected surplus, chosen such that the portfolio can be considered stable. In this paper, we present an alternative model for the premium pricing process of a portfolio consisting of different non-life products. Moreover, a standard decision function for the determination of the premium is proposed based on the recent claim experience and a negative feedback mechanism of the known surplus value. The investigation of the robust stability of the system is performed via a Linear Matrix Inequality (LMI) criterion, permitting extensions of existing results. The novelty of the approach consists in the use of tools from the robust analysis of engineering systems in the insurance pricing process of non-life products into a discrete-time framework. Keywords Non-life insurance Pricing process Robust stability LMI techniques
1 Introduction One of the most significant quite complicated and challenging problems in Actuarial Science, and especially for general insurance products, is the premium pricing process. A fundamental issue of this process is to provide an accurate pricing model A. A. Pantelous (&) Institute for Financial and Actuarial Mathematics (IFAM), Department of Mathematical Sciences and Institute for Risk and Uncertainty, University of Liverpool, Liverpool L69 7ZL, UK e-mail: [email protected] A. Papageorgiou School of Engineering and Mathematical Sciences, City University, London, UK
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under this uncertain framework. Therefore, the actuary should understand the financial environment and constraints facing his insurance organization, the stochastic nature of the different variables involved, the market completion and the different delays in collecting the appropriate information. These are some of the most key modelling characteristics used in the insurance pricing models. In insurance industry, the pooling of risk is a fundamental condition for general insurance products; see for instance Booth et al. [4], Zaks et al. [17], and Pantelous et al. [13]. However, from the point of view of managing the different types of risks, it is significant to distinguish them among policyholders with diverse risk characteristics and preferences (i.e. creating different clusters). Actually, precise knowledge of the different risk characteristics of its policyholders enables the insurer to attribute costs fairly between them, and to protect itself from antiselection by proposers. Finally, the actuarial aspect of a premium calcul
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