On Multivariate Prudence

In this paper we extend the theory of precautionary saving to the case in which uncertainty is multidimensional and we develop a matrix-measure of multivariate prudence. Furthermore, we characterize comparative prudence, decreasing and increasing prudence, the effect of uncertainty on the marginal propensity to consume out of wealth, and the Drèze-Modigliani substitution effect in this multivariate setting. We also characterize the concept of multivariate downside risk aversion as a multivariate preference for harm disaggregation. We show that our definition is equivalent to a positive precautionary saving motive. We propose an alternative measure of the intensity of downside risk aversion and show that this measure is useful in understanding several economic problems that involve multivariate preferences.matrix-measure, multivariate prudence, comparative prudence, multivariate downside risk aversion, downside risk aversion, multivariate preferences

Comparative Ross Risk Aversion in the Presence of Mean Dependent Risks

This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Although the literature covers this question extensively, our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessary mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross (1981) for mean independent risks. Finally, we show that decreasing cross Ross risk aversion gives rise to the utility function family belonging to the class of n-switch utility functions.Comparative cross Ross risk aversion, Dependent background risk, Partial risk premium, Decreasing cross Ross risk aversion, n-switch utility function

Agricultural Risk Aversion Revisited: A Multicriteria Decision-Making Approach

In modelling farm systems it is widely accepted that risk plays a central role. Furthermore, farmers' risk aversion determines their decisions in both the short and the long run. This paper presents a methodology based on multiple criteria mathematical programming to obtain relative and absolute risk aversion coefficients. We rely on multiattribute utility theory (MAUT) to elicit a separable additive multiattribute utility function and then estimate the risk aversion coefficients and apply this methodology to an irrigated area of Northern Spain. The results show a wide variety of attitudes to risk among farmers, who mainly exhibit decreasing absolute risk aversion (DARA) and constant relative risk aversion (CRRA).Risk analysis, Agriculture, Utility theory, Multiple criteria analysis, Risk and Uncertainty,

Comparative risk aversion when the outcomes are vectors

Pratt (1964) and Yaari (1969) contain the classical results pertaining to the equivalence of various notions of comparative risk aversion of von Neumann-Morgenstern utilities in the setting with real-valued outcomes. Some of these results have been extended to the setting with outcomes inComparative risk aversion, vector space of outcomes, acceptance set, vector-valued risk premia, vector-valued Arrow-Pratt coefficient, Pettis integral, ordered topological vector spaces, ordered Hilbert spaces

Rotating Savings and Credit Associations as Insurance

Recent theoretical research on rotating savings and credit associations (Roscas) suggests that identical individuals prefer a random to a bidding Rosca when participants save for a lumpy durable or an investment good. Here,in contrast, under the assumption that participants are risk averse and that their incomes are stochastic and independent, it is shown that a random Rosca is not advantageous, while participation in a bidding Rosca improves ex ante expected utility if temporal risk aversion is less pronounced than static risk aversion. When information on individual incomes is private, fixed contributions to a bidding Rosca help to mitigate the problem of information asymmetries. When information on incomes is public, a lack of enforceability of variable contributions may explain the existence of Roscas instead of more efficient insurance arrangements.

Reduced perplexity: Uncertainty measures without entropy

Conference paper presented at Recent Advances in Info-Metrics, Washington, DC, 2014. Under review for a book chapter in "Recent innovations in info-metrics: a cross-disciplinary perspective on information and information processing" by Oxford University Press.A simple, intuitive approach to the assessment of probabilistic inferences is introduced. The Shannon information metrics are translated to the probability domain. The translation shows that the negative logarithmic score and the geometric mean are equivalent measures of the accuracy of a probabilistic inference. Thus there is both a quantitative reduction in perplexity as good inference algorithms reduce the uncertainty and a qualitative reduction due to the increased clarity between the original set of inferences and their average, the geometric mean. Further insight is provided by showing that the Renyi and Tsallis entropy functions translated to the probability domain are both the weighted generalized mean of the distribution. The generalized mean of probabilistic inferences forms a Risk Profile of the performance. The arithmetic mean is used to measure the decisiveness, while the -2/3 mean is used to measure the robustness

Does Risk Seeking Drive Asset Prices? A stochastic dominance analysis of aggregate investor preferences

We investigate whether risk seeking or non-concave utility functions can help to explainthe cross-sectional pattern of stock returns. For this purpose, we analyze the stochasticdominance efficiency classification of the value-weighted market portfolio relative tobenchmark portfolios based on market capitalization, book-to-market equity ratio andmomentum. We use various existing and novel stochastic dominance criteria that accountfor the possibility that investors exhibit local risk seeking behavior. Our results suggestthat Markowitz type utility functions, with risk aversion for losses and risk seeking forgains, can capture the cross-sectional pattern of stock returns. The low average yield onbig caps, growth stocks and past losers may reflect investors' twin desire for downsideprotection in bear markets and upside potential in bull markets.asset pricing;stochastic dominance;prospect theory;risk seeking;specification error