Pooling and Valuation Revisited

Concerning the economic losses associated with the COVID-19 outbreak and other recent large catastrophes, and given that in a connected world the economic losses have a larger impact, we aim to revisit the fundamental insurance paradigms, in particular, pooling and valuation in the presence of systematic risk. We consider a pool of policyholders whose losses can be widely correlated through common shock. We have observed that from a mathematical standpoint, insurance as a pooling approach can manage the risk if the principle of insurance (POI), that is to keep the systematic risk secure, holds. Our study suggests that valuation cannot be independent of the risk pool, and the premium needs to be adjusted according to the systematic safety loading. This also motivates the introduction of ex-post policies that can vanish the systematic safety loading by introducing contingent premiums. In addition, we look at the upper bounds for the pool valuation when the pool is influenced by a common shock. In the end, we make an assessment of our theory with two examples, first the UK Coronavirus job retention case and second catastrophe events in the agricultural sector. This way we propose a novel way to analyze events with large economic losses.