Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Abstract

Abstract:The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products, we challenge the de nition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with risk measures as considered in the SII framework and then proceed with the ruin theory approach. Instead of considering the continuous time setting of the ruin theory, we consider the discrete time-the yearly basis-of the accounting viewpoint. Wenally give an illustration with a xed guaranteed rate product along with the equity, interest rate and longevity risks. The latter risk brings us to consider zero-coupon longevity bonds in which we invest the capital. We show that long-term guarantees might be overloaded under the SII regulation.

Impact of the choice of risk assessment time horizons on defined benefit pension schemes

“…There is relatively little research on the impact of the time horizon on pension risk quantification. One recent attempt is Devolder & Lebegue (2016), who used ruin theory to estimate the solvency capital requirement for long-term life insurance and pension products, arguing that the 1-year horizon of the Solvency II framework may not be appropriate for products with long terms. Using a simple model, the authors showed that under the Solvency II framework, solvency capital is understated at shorter durations and overstated at longer durations, citing inadequacy of the Solvency II framework to account for benefits of long-term equity investments.…”

Compositions of Conditional Risk Measures and Solvency Capital

“…The inclusion of the interest rate and longevity risks has been considered in [14] with static risk measures. However, the inclusion of these risks in our dynamic setting would require the use of numerical techniques in order to compute the solvency capital, while the framework that we consider here allows us to obtain closed-form formulae.…”