Risk-Sharing and Contingent Premia in the Presence of Systematic Risk: The Case Study of the UK COVID-19 Economic Losses

Abstract

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management platforms and study efficient insurance schemes in the presence of systematic events. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we show that under a non-discriminatory insurance assumption, it is optimal for everybody to bear the average final wealth. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. As a result, an efficient solution is generated in the risk-sharing platform where insurance is a mechanism to redistribute the wealth. Second, we show that in an insurance platform, where the insurance is regulated, we see that there is a need for a social insurance scheme to bear the risk of the tail events. Third, in a competitive market we see how a classical solution can raise the risk of insolvency and in a decentralised market the equilibrium cannot be reached if there is adequate sensitivity to the systematic risks. In addition, we have encountered our theory to a case where the losses are calibrated based on the UK furlough scheme during the COVID-19 pandemic and measure the level of insolvency risk and the market failure.