Bridging the gap between risk and uncertainty in insurance

Abstract

This contribution evokes Orio Giarini’s courage to think ‘outside the box’. It proposes a practical way to bridge the gap between risk (where probabilities of occurrence are fully known) and uncertainty (where these probabilities are unknown). However, in the context of insurance, neither extreme applies: the risk type of a newly enrolled customer is not fully known, loss distributions (especially their tails) are difficult to estimate with sufficient precision, the diversification properties of a block of policies acquired from another company can be assessed only to an approximation, and rates of return on investment depend on decisions of central banks that cannot be predicted too well. This contribution revolves around the launch of an innovative insurance product, where the company has a notion of whether a favourable market reception is more likely than an unfavourable one, of the chance of obtaining approval from the regulatory authority and the risk of a competitor launching a similar innovation. Linear partial information theory is proposed and applied as a particular practical way to systematically exploit the imprecise information that may exist for all of these aspects. The decision-making criterion is maxEmin, an intuitive modification of the maximin rule known from games against nature.