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Control Theory and Insurance Systems

Zimbidis, A. (1999). Control Theory and Insurance Systems. (Unpublished Doctoral thesis, City, University of London)


The primary target of the current thesis is the establishment of a link (bridge) between the abstract concepts of control theory and the practical applications connected with different insurance systems. The existence of such a link has been identified by several authors in the last two decades who have focused on the use of conventional control theory (and optimal control techniques) in actuarial problems.

In our approach, after providing a short reference guide to the modern control theory in chapter 2 and a selective review of the literature in chapter 3, we propose three distinct models covering the most important areas of insurance applications (i.e. Life, General Insurance & Pensions). From the control point of view we actually use all the potential tools i.e. Multiple Input - Multiple Output, Time-Varying format, Nonlinear equations, Stability Analysis, Root Locus Method, Optimal design for the parameters involved and optimal control of a dynamic system.

The thesis deals with the basic concept of an insurance system, "the premium" and aims to answer the critical question "How to calculate and control the premium rating process?".

In the first model (chapter 4), we examine the general process of insurance pricing, using the standard equation which connects the three major variables involved i.e. premiums, claims & surplus. Starting from the roots of actuarial science and the static point of view and passing to Lundberg’s revolution with his dynamic view, we arrive at the modern alternative view of control theory with respect to pricing models. We concentrate to the concept of stability rather than to the traditional concept of ruin.

In the second model (chapter 5), we construct a dynamic system which describes a special reinsurance arrangement (multinational pooling) which may only be handled using the modern control theory (as it refers to a multivariable system). Actually it is an extension of the previous model to a multi-system which consists of different subsystems, as described in chapter 4 considering also the interaction between them.

Finally in the third model (chapter 6) we investigate the philosophy and mechanisms of the Social Security System and the PAYG funding method. It may also be seen as an extension of the first model to the area of pensions and the necessity of calculating and controlling the respective contribution rate and the age of normal retirement. At the end of the sixth chapter, a simulation is carried out for the projected population data of Greece up to the year 2020.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance > Actuarial Research Reports
Bayes Business School > Bayes Business School Doctoral Theses
Doctoral Theses
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