Expected utility without utility

This paper advances an interpretation of Von Neumann–Morgenstern’s expected utility model for preferences over lotteries which does not require the notion of a cardinal utility over prizes and can be phrased entirely in the language of probability. According to it, the expected utility of a lottery can be read as the probability that this lottery outperforms another given independent lottery. The implications of this interpretation for some topics and models in decision theory are considered.expected utility, cardinal utility, benchmark, risk attitude, stochastic dominance

Insurance Premia Consistent with the Market.

We consider insurance prices in presence of an incomplete and competitive market. We show that if the insurance price system is internal, sublinear, and consistent with the market, then insurance prices are the maxima of their expected payments with respect to a family of risk neutral probabilities. We also show that under a simple additional assumption it is possible to decompose the obtained price in net premium plus safety loading.

Star-shaped Risk Measures

In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity property of coherent risk measures is dispensed with and positive homogeneity is weakened, include all practically used risk measures, in particular, both convex risk measures and Value-at-Risk. From a financial viewpoint, our relaxation of convexity is necessary to quantify the capital requirements for risk exposure in the presence of liquidity risk, competitive delegation, or robust aggregation mechanisms. From a decision theoretical perspective, star-shaped risk measures emerge from variational preferences when risk mitigation strategies can be adopted by a rational decision maker

Benchmarking real-valued acts

A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional V (f) = P(f \ge β). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P

Sul principio di Bernoulli

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La produzione scientifica di Eugenio Levi

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Sublinear functionals and prices

We consider sublinear functionals and we characterise their positivity and monotonicity, showing that such properties represent very natural features for price systems

On generalised transforms of distribution functions

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