[Asymmetric information between banks and firms can preclude financing of valuable projects. Trade credit can alleviate this problem by incorporating in the lending relation the private information held by suppliers about their customers. Incentive compatibility conditions prevent collusion between two of the agents (e.g., the buyer and the seller) against the third (e.g., the bank). Consistent with the empirical findings of Petersen and Rajan (1995), firms without relationships with banks resort more to trade credit, and sellers with greater ability to generate cash flows provide more trade credit. Finally small firms react to monetary contractions by using trade credit, consistent with the empirical results of Nilsen (1994).]

This paper investigates the comparative statics of “more ambiguity aversion” as defined by <cross-ref type="bib" refid="bib26">Klibanoff, Marinacci and Mukerji (2005</cross-ref>, “A Smooth Model of Decision Making under Ambiguity”, Econometrica , 73 (6), 1849–1892). The analysis uses the static two-asset portfolio problem with one safe asset and one uncertain one. While it is intuitive that more ambiguity aversion would reduce demand for the uncertain asset, this is not necessarily the case. We derive sufficient conditions for a reduction in the demand for the uncertain asset and for an increase in the equity premium. An example that meets the sufficient conditions is when the set of plausible distributions for returns on the uncertain asset can be ranked according to their monotone likelihood ratio. It is also shown how ambiguity aversion distorts the price kernel in the alternative portfolio problem with complete markets for contingent claims.

In the standard portfolio problem, a shift in the distribution of the risky asset is “portfolio-dominated” if it reduces the demand for the risky asset by all risk-averse agents, irrespective of the risk-free rate. We show that the condition obtained by Landsberger and Meilijson (1993), while necessary, is not sufficient for portfolio dominance and we present an exact necessary and sufficient condition.

In a growing economy, the discount rate to evaluate a long-term investment is the minimum rate of expected return that compensates for the increased intergenerational inequalities. Because the growth rate is uncertain, there is a precautionary argument in favor of lowering the discount rate. If shocks to growth are persistent, this is a robust argument for using a smaller discount rate for more distant time horizons. If climate damages are positively correlated with future consumption, a risk premium should be added to the climate discount rate, which could have an increasing term structure.

Asymmetric information between banks and firms can preclude financing of valuable projects. Trade credit can alleviate this problem by incorporating in the lending relation the private information held by suppliers about their customers. Incentive compatibility conditions prevent collusion between two of the agents (e.g., the buyer and the seller) against the third (e.g., the bank). Consistent with the empirical findings of Petersen and Rajan (1995), firms without relationships with banks resort more to trade credit, and sellers with greater ability to generate cash flows provide more trade credit. Finally small firms react to monetary contractions by using trade credit, consistent with the empirical results of Nilsen (1994).

We examine in this paper a new natural restriction on utility functions, namely that adding an unfair background risk to wealth makes risk-averse individuals behave in a more risk-averse way with respect to any other independent risk. This concept is called risk vulnerability. It is equivalent to the condition that an undesirable risk can never be made desirable by the presence of an independent, unfair risk. Moreover, under risk vulnerability, adding an unfair background risk reduces the demand for risky assets. Risk vulnerability generalizes the concept of properness (individually undesirable, independent risks are always jointly undesirable) introduced by Pratt and Zeckhauser (1987). It implies that the two first derivatives of the utility function are concave transformations of the original utility function. Under decreasing absolute risk aversion, a sufficient condition for risk vulnerability is local properness, i.e. r'' ≥ r'r, where r is the Arrow-Pratt coefficient of absolute risk aversion.

ECONOMIC DECISION MAKING UNDER UNCERTAINTY often takes place in the presence of multiple and in markets that are less than complete. As a consequence, choices about endogenous sometimes must be made while simultaneously facing one or more immutable exogenous risks that are not under the control of the agent, and that are independent of endogenous risks. It is somehow natural to assume that an exogenous deterioration in background wealth will cause an individual to take more care elsewhere. If we define a deterioration, for example, as making the individual poorer by removing a fixed amount of initial wealth, we know from Pratt (1964) that decreasing absolute risk aversion (DARA) of an individual's von Neumann-Morgenstern utility function yields this natural result. If, on the other hand, background wealth becomes riskier due to the addition of a zero-mean risk, that is also statistically independent of all other risks, behavior will be more risk averse if and only if preferences are risk vulnerable as defined by Gollier and Pratt (1996). Risk vulnerability (described below in Section 4) is a stronger notion than DARA and includes proper risk aversion (Pratt and Zeckhauser (1987)) and standard risk aversion (Eeckhoudt and Kimball (1992), Kimball (1993)) as particular cases. But a deterioration in background wealth may encompass more complicated distribution changes than the introduction of another statistically independent risk. In this paper, we examine background wealth deteriorations that take the form of both general firstand second-degree stochastic dominance changes in risk (FSD and SSD respectively). In particular, we determine conditions that are both necessary and sufficient for each of these two types of background risk changes to imply more risk-averse behavior on the part of the individual. For the case of FSD changes, this condition turns out to be Ross' stronger characterization of decreasing absolute risk aversion. In the case of general SSD changes in the distribution of background wealth, the condition derived is a stronger version (in Ross' sense) of the conditions characterizing preferences that are locally risk vulnerable in the sense of Gollier and Pratt. The necessary and sufficient conditions derived are fairly restrictive upon preferences. However, if we take as positive behavior that individuals act in a more risk-averse manner whenever the distribution of background wealth deteriorates, these conditions place canonical limits upon appropriate utility representations. At the very least, they

Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns by Markus K. Brunnermeier, Christian Gollier and Jonathan A. Parker. Published in volume 97, issue 2, pages 159-165 of American Economic Review, May 2007

We examine an economy whose consumers have different discount factors for utility, possibly not exponential. We characterize the properties of efficient allocations of resources and of the shadow prices that would decentralize such allocations. We show in particular that the representative agent has a decreasing discount rate when, as is usually posited, all of a group’s members have a constant discount rate and decreasing absolute risk aversion preferences. We also identify conditions that lead the representative agent to have a rate of impatience that decreases with gross domestic product per capita.