Systematic risk in long-term insurance business.

The classical approach to manage insurance risk consists in selling a sufficiently large number of policies. This strategy allows the insurer to reduce the variations of the claim payments per-policy around the corresponding theoretical mean. Nevertheless, the insurer remains exposed to a systematic risk which cannot be completely eliminated by increasing the portfolio size. The presence of this risk is essentially due to the fact that the two components of the claim payment, i.e. the claim amount and its probability of occurrence, may be time-varying and subject to uncertainty. Managing this risk is all the more important in the context of long-term insurance business, where the premium estimate at policy issue has to account for the unpredictable changes in the underlying risk factors. In this thesis, we address systematic risk in long-term insurance business which stems from the uncertainty on the claim amount (medical inflation risk) and on the probability of the benefit payment (longevity and mortality risks). Part 1 is devoted to the management of medical inflation risk in Belgian private health insurance contracts. The Belgian legislator introduced in 2007 a mechanism allowing insurers to transfer medical inflation risk back to policyholders via premium adjustments. Our contribution is threefold. First, we focus on the medical index, which captures the evolution of claim amounts over time. We highlight some deficiencies in its current construction. We also propose an alternative method which accounts for the heterogeneity in the structure of products sold in the Belgian market, while satisfying to some extent the transparency requirement of consumers' representatives. Second, we focus on the adjustment mechanism, whose goal is to include in the contract elements the information on medical inflation over time. We derive actuarially fair mechanisms to assess the adjustment rule prescribed by the Belgian regulator in the Royal Decree of 18 March 2016. Our analysis shows that the Belgian rule often leads to conservative premium adjustments from the viewpoint of the insurer. We also find that this rule may be insufficient under some scenarios of medical inflation and interest rate. Third, we discuss some remaining challenges in the Belgian system with a focus on the transferability of the reserve and on age discrimination. We also provide recommendations to enhance the Belgian system and ensure more protection for policyholders, taking into account the solvency constraint of insurers. In Part 2, we address the management of longevity risk in long-term insurance business. We further analyze the solution consisting in transferring the systematic risk back to policyholders. We extend the existing literature by considering a situation where only part of the risk is transferred, and hence, the risk sharing mechanism is not limited to the no-transfer/full-transfer binarism. We propose a dynamic equivalence principle, and derive updating rules for the contract elements. We compare contacts managed with the proposed risk sharing scheme and their classical counterparts. Our setting allows us to derive conditions for a viable risk sharing scheme, such that both the insurer and policyholders are better off by sharing the risk over time. Finally, Part 3 considers the interplay between longevity and mortality risks, and we compare the case where the offsetting relationship between these two risks is exploited in the pricing (i.e. joint pricing), with the case where it is not exploited (i.e. stand-alone pricing). We highlight several challenges for insurer's relying on joint pricing. In particular, we show that for the less risky business line, the required loaded premium in case of joint pricing can be higher than its counterpart in case of stand-alone pricing. We also find that the choice of competitiveness comes with the burden of portfolio monitoring. Moreover, for the same level of risk, our analysis suggests that switching from the stand-alone to the joint pricing may lead to a decrease of the total collected premiums.

Publication year:2019

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