Delay-Dependent Robust Stability Analysis for Premium-Reserve Models in an Arbitrary Regime Switching Discrete-Time Framework

Abstract

In the insurance industry, the actuarial team experiences significant challenges for pricing a competitive but also fair premium and keeping an accurate level of reserve, which leads inevitably to numerous adjustments over time and potentially several millions of US dollars in annual losses. Because the model and parameter uncertainties play key roles for actuaries, decision makers, and policymakers, the implementation of advanced mathematical and statistical techniques is highly required. Over the last two decades, applications of regime switching models to finance and economics have received strong attention among researchers and particularly among market practitioners. This paper attempts to consider how a linear arbitrary regime switching system in discrete-time framework could be applied to calculate the medium- and long- term reserves and the relevant premiums (abbreviated here as the P-R process) from the point of view of an insurer. In this direction, some recently developed techniques from linear robust control theory are applied to explore the stability, stabilization, 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 this treatment. Finally, a numerical example is illustrated.