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

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management setups and study efficient insurance schemes in the presence of low probability shock events that trigger losses for all participants. 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 equally share all risk in the market. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. Insurance is then a mechanism to redistribute wealth, and we call this a risk-sharing solution. Second, we show that in an insurance platform, where the insurance is regulated, the tail events are not shared, but borne by the government. Third, in a competitive market we see how a classical solution can raise the risk of insolvency. Moreover, in a decentralised market, the equilibrium cannot be reached if there is adequate sensitivity to the common shock events. In addition, we have applied our theory to a case where the losses are calibrated based on the UK Coronavirus Job Retention Scheme.