Bruno de Finetti’s encounter with martingales

The British Journal for the Philosophy of Science, 2012

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 precise 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 Lloyd's of London proves that this is so even in practice. The purpose of this paper 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. 2 Knight and Keynes on the philosophy of unknown probabilities and Lloyd's 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

Economic and Financial Decisions under Risk, 2011

Brazilian Review of Econometrics, 2001

This article condenses the theory for the valuation of contingent claims in complete and arbitrage-free markets by means of martingales The main focus is centered on markets in which it is possible to negotiate at any time; that is, markets whose history takes place at a continuous time. Resumo Este artigo condensa a teoria de avalia<;ao de tltulos contingentes em mer cados completos e livres de arbitragem por meio de martingais. To cl a a aten<;ao esta voltada para mercados cnde e possivel negociar em qualquer instante do tempo, isto €i, mercados cuja hist6ria se desenvolve em tempo continuo.

2010

In the insurance literature it is often argued that private markets can provide insurance against 'risk' 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 precise 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 Lloyd's of London proves that this is so even in practice. The purpose of this paper is to show that Bruno de Finetti, widely regarded 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.

Canadian Journal of Philosophy, 2015

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate.

In this paper we discuss the role of de Finetti as a forerunner of some of the more relevant concepts and tools of the modern theory of finance. It is shown that de Finetti gave some ground breaking contributions in such fields as arbitrage free pricing, mean variance efficiency, expected utility and risk aversion. We think it is not only a matter of historical remarks: indeed some of his ideas reveal to be fruitful even nowadays so that going on studying de Finetti&#39;s papers may be a good investment for those interested in quantitative finance and economics of uncertainty. Acknowledgement. We acknowledge financial support of MedioCredito FVG through the &quot;B.

Decision-making Process, 2009

Ce chapitre d'ouvrage collectif a pour but de présenter les bases de la modélisation de la prise de décision dans un univers risqué. Nous commençons par dé…nir, de manière générale, la notion de risque et d'accroissement du risque et rappelons des dé…nitions et catégorisations (valables en dehors de tout modèle de représentation) de comportements face au risque. Nous exposons ensuite le modèle classique d'espérance d'utilité de von Neumann et Morgenstern et ses principales propriétés. Les problèmes posés par ce modèle sont ensuite discutés et deux modèles généralisant l'espérance d'utilité brièvement présentés. Mots clé: risque, aversion pour le risque, espérance d'utilité, von Neumann et Morgenstern, Paradoxe d'Allais. JEL: D81

Insurance: Mathematics and Economics, 2013

Probability statements about future evolutions of …nancial and actuarial risks are expressed in terms of the 'real-world' probability measure P, whereas in an arbitrage-free environment, the prices of these traded risks can be expressed in terms of an equivalent martingale measure Q. The assumption of independence between …nancial and actuarial risks in the real world may be quite reasonable in many situations. Making such an independence assumption in the pricing world however, may be convenient but hard to understand from an intuitive point of view. In this pedagogical paper, we investigate the conditions under which it is possible (or not) to transfer the independence assumption from P to Q. In particular, we show that an independence relation that is observed in the P-world can often not be maintained in the Q-world.

Insurance: Mathematics and Economics, 1996

The non-expected-utility tbeories of decision under risk have fovond the appearance of new notions of incieasing risk like ntonotone increasing risk (based on the notion of comonotonic random vahablcs) or new notions of risk aversion like averaion to monotone increasing risk, in better agreement witb tbese new theories. After a survey of atl tbc possible notions of increasing risk and of risk aversion and tbeir intrinsic de^nitions, we show tbat cODtivy to expected-utility tbeory where all the notions of risk avenion bave the same characterization (u concave), in the ftunework of rank-dependent expected utility (one of the most well known of the non-expectedutility models), tbe characterizations of all these notions of risk aversion are different. Moreover, we sbow tbat, even in tbe expected-utility framcworic, the new notion of monotone increasing risk can give better answers to some pn^lems of comparative sutics sucb as in ponfoUo cboice or in partial insurance. This new notion also can suggest more intuitive approaches to inequalities measurement.