Preserving preference rankings under non-financial background risk

We investigate the impact of a non-financial background risk ˜" on the preference rankings between two independent financial risks ˜z1 and ˜z2 for an expected-utility maximizer. More precisely, we provide necessary and sufficient conditions for the alternative (x0 + ˜z1, y0 + ˜") to be preferred to (x0 + ˜z2, y0 + ˜") whenever (x0 + ˜z1, y0) is preferred to (x0 + ˜z2, y0). Utility functions that preserve the preference rankings are fully characterized. Their practical relevance is discussed in light of recent results on the constraints for the modeling of the preference for the disaggregation of harms.Multivariate risk, Background risk, Disaggregation of harms, Risk independence

Preserving preference rankings under non-financial background risk

International audienceWe investigate the impact of a non-financial background risk ˜" on the preference rankings between two independent financial risks ˜z1 and ˜z2 for an expected-utility maximizer. More precisely, we provide necessary and sufficient conditions for the alternative (x0 + ˜z1, y0 + ˜") to be preferred to (x0 + ˜z2, y0 + ˜") whenever (x0 + ˜z1, y0) is preferred to (x0 + ˜z2, y0). Utility functions that preserve the preference rankings are fully characterized. Their practical relevance is discussed in light of recent results on the constraints for the modeling of the preference for the disaggregation of harms

Heterogeneous expectations and long range correlation of the volatility of asset returns

Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection between the distributional properties of the heterogeneity parameters and the auto-covariance/auto-correlation functions of the realized volatility. We report different behaviors, or change of convention, whose observation depends on the market phase under consideration. In particular, we report and justify the fact that the volatility exhibits significantly longer memory during the phases of speculative bubble than during the phase of recovery following the collapse of a speculative bubble

Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal

We address the general problem of testing a power law distribution versus a log-normal distribution in statistical data. This general problem is illustrated on the distribution of the 2000 US census of city sizes. We provide definitive results to close the debate between Eeckhout (2004, 2009) and Levy (2009) on the validity of Zipf's law, which is the special Pareto law with tail exponent 1, to describe the tail of the distribution of U.S. city sizes. Because the origin of the disagreement between Eeckhout and Levy stems from the limited power of their tests, we perform the {\em uniformly most powerful unbiased test} for the null hypothesis of the Pareto distribution against the lognormal. The $p$-value and Hill's estimator as a function of city size lower threshold confirm indubitably that the size distribution of the 1000 largest cities or so, which include more than half of the total U.S. population, is Pareto, but we rule out that the tail exponent, estimated to be $1.4 \pm 0.1$, is equal to 1. For larger ranks, the $p$-value becomes very small and Hill's estimator decays systematically with decreasing ranks, qualifying the lognormal distribution as the better model for the set of smaller cities. These two results reconcile the opposite views of Eeckhout (2004, 2009) and Levy (2009). We explain how Gibrat's law of proportional growth underpins both the Pareto and lognormal distributions and stress the key ingredient at the origin of their difference in standard stochastic growth models of cities \cite{Gabaix99,Eeckhout2004}.Comment: 7 pages + 2 figure

On Cross-risk Vulnerability

International audienceWe introduce the notion of cross-risk vulnerability to generalize the concept of risk vulnerability introduced by Gollier and Pratt [Gollier, C., Pratt, J.W. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109–1124]. While risk vulnerability captures the idea that the presence of an unfair financial background risk should make risk-averse individuals behave in a more risk-averse way with respect to an independent financial risk, cross-risk vulnerability extends this idea to the impact of a non-financial background risk on the financial risk. It provides an answer to the question of the impact of a background risk on the optimal coinsurance rate and on the optimal deductible level. We derive necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also analyze the question of the sub-additivity of risk premia and show to what extent cross-risk vulnerability provides an answer

Preparing for the Worst : Incorporating Downside Risk in Stock Market Investments

International audienc

Book review : "Why Stock Market Crash?" by D. Sornette (Princeton University Press)

International audienc