Alberto Feduzi

De Finetti on the insurance of risks and uncertainties

In the insurance literature, it is often argued that private markets can provide insurance against ‘risks’ but not against ‘uncertainties’ in the sense of Knight ([1921]) or Keynes ([1921]). This claim is at odds with the standard economic model of risk exchange which, in assuming that decision-makers are always guided by point-valued subjective probabilities, predicts that all uncertainties can, in theory, be insured. Supporters of the standard model argue that the insuring of highly idiosyncratic risks by Lloyds of London proves that this is so even in practice. The purpose of this article is to show that Bruno de Finetti, famous as one of the three founding fathers of the subjective approach to probability assumed by the standard model, actually made a theoretical case for uncertainty within the subjectivist approach. We draw on empirical evidence from the practice of underwriters to show how this case may help explain the reluctance of insurers to cover highly uncertain contingencies. 1 Introduction 2 Knight and Keynes on the Philosophy of Unknown Probabilities and Lloyds of London   2.1 Knight   2.2 Keynes 3 Insuring Unique Events: The Subjectivist Viewpoint as Represented by de Finetti 4 The ‘Philosophy’ of Practitioners 5 De Finetti on Uncertainty in Knight and Keynes and on Insurability   5.1 De Finetti on Knight   5.2 De Finetti on Keynes 6 Empirical Evidence on Insurance Under Ambiguity 7 Conclusion 1 Introduction 2 Knight and Keynes on the Philosophy of Unknown Probabilities and Lloyds of London   2.1 Knight   2.2 Keynes   2.1 Knight   2.2 Keynes 3 Insuring Unique Events: The Subjectivist Viewpoint as Represented by de Finetti 4 The ‘Philosophy’ of Practitioners 5 De Finetti on Uncertainty in Knight and Keynes and on Insurability   5.1 De Finetti on Knight   5.2 De Finetti on Keynes   5.1 De Finetti on Knight   5.2 De Finetti on Keynes 6 Empirical Evidence on Insurance Under Ambiguity 7 Conclusion

Unknowns, Black Swans and the risk/uncertainty distinction

Tony Lawson’s work on probability and uncertainty is both an important contribution to the heterodox canon as well as a notable early strand of his ongoing enquiry into the nature of social reality. In keeping with most mainstream and heterodox discussions of uncertainty in economics, however, Lawson focuses on situations in which the objects of uncertainty are imagined and can be stated in a way that, potentially at least, allows them to be the subject of probability judgments. This focus results in a relative neglect of the kind of uncertainties that flow from the existence of possibilities that do not even enter the imagination and which are therefore ruled out as the subject of probability judgments. This paper explores uncertainties of the latter kind, starting with and building on Donald Rumsfeld’s famous observations about known unknowns and unknown unknowns. Various connections are developed, first with Nassim Taleb’s Black Swan, and then with Lawson’s Keynes-inspired interpretation of uncertainty.

De Finetti and Savage on the normative relevance of imprecise reasoning: a reply to Arthmar and Brady

This paper examines the claim that de Finetti and Savage completely rejected the notion of indeterminate, as distinct from imprecise, probabilities. It argues that their examination of imprecise reasoning refers both to descriptive and normative issues, and that the inability for a decisionmaker to commit to a single prior cannot be limited to measurement problems, as argued by Arthmar and Brady in a recent contribution to this Journal. The paper shows that de Finetti and Savage admitted that having an interval of initial probabilities may sometimes have normative relevance, thereby leaving an opening for indeterminate probabilities.