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Putting Risk in Its Proper Place

American Economic Review 2006 96(1), 280-289
This paper examines preferences toward particular classes of lottery pairs. We show how such concepts as prudence and temperance can be fully characterized by a preference relation over these lotteries. If preferences are defined in an expectedutility framework with differentiable utility, the direction of preference for a particular class of lottery pairs is equivalent to signing the n th derivative of the utility function. What makes our characterization appealing is its simplicity, which seems particularly amenable to experimentation.

Optimal Insurance in Incomplete Markets

Journal of Political Economy 1983 91(6), 1045-1054
This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.

Optimal Insurance in Incomplete Markets

Journal of Political Economy 1983 91(6), 1045-1054
This paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk. Existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions. In particular, conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks. These results may provide a partial explanation why existing theory is often contradicted by observable behavior.

Optimal Hedging under Intertemporally Dependent Preferences

Journal of Finance 1990 45(4), 1315
This paper examines optimal hedging behavior in a market where preferences for current consumption are partly determined by the consumer's past consumption history. The model considers an individual exposed to price risk, who allocates wealth between consumption and futures contracts over a (continuous-time) finite planning horizon. The speculative component of the hedge ratio is shown to be smaller and the consumption path smoother than in models where preferences are separable over time. Some comparative-static properties of the hedge ratio are also examined.

Optimal Hedging under Intertemporally Dependent Preferences

Journal of Finance 1990 45(4), 1315-1324
This paper examines optimal hedging behavior in a market where preferences for current consumption are partly determined by the consumer's past consumption history. The model considers an individual exposed to price risk, who allocates wealth between consumption and futures contracts over a (continuous‐time) finite planning horizon. The speculative component of the hedge ratio is shown to be smaller and the consumption path smoother than in models where preferences are separable over time. Some comparative‐static properties of the hedge ratio are also examined.

Optimal Hedging Under Intertemporally Dependent Preferences.

Journal of Finance 1990 45(4), 1315-24
This paper examines optimal hedging behavior in a market where preferences for current consumption are partly determined by the consumer's past consumption history. The model considers an individual exposed to price risk, who allocates wealth between consumption and futures contracts over a (continuous-time) finite planning horizon. The speculative component of the hedge ratio is shown to be smaller and the consumption path smoother than in models where preferences are separable over time. Some comparative-static properties of the hedge ratio are also examined.

Exploring Higher Order Risk Effects

Review of Economic Studies 2010 77(4), 1403-1420
Precautionary saving has been linked to the property of prudence, and the property of temperance has been used to show how the presence of an unavoidable risk affects one's behaviour towards a second risk. These two higher order risk effects also play key roles in aversion to negative skewness and to kurtosis, respectively. This article presents a laboratory experiment to determine whether subjects are prudent and/or temperate. The experiment is based upon preferences over lottery pairs in simple 50–50 gambles. Subjects are asked in which of two states of nature they would prefer to receive a zero-mean gamble. For prudence, the choices are between a lower and higher wealth outcome. For temperance, the choices are between a state with no other risk and a state with a second (independent) risk. The results show behavioural evidence for prudence, but they also show evidence of intemperate behaviour. Implications of these results for both expected-utility and non-expected-utility models are examined.

Consistency of Higher Order Risk Preferences

Econometrica 2014 82(5), 1913-1943
Risk aversion (a second-order risk preference) is a time-proven concept in economic models of choice under risk. More recently, the higher order risk preferences of prudence (third-order) and temperance (fourth-order) also have been shown to be quite important. While a majority of the population seems to exhibit both risk aversion and these higher order risk preferences, a significant minority does not. We show how both risk-averse and risk-loving behaviors might be generated by a simple type of basic lottery preference for either (1) combining “good” outcomes with “bad” ones, or (2) combining “good with good” and “bad with bad,” respectively. We further show that this dichotomy is fairly robust at explaining higher order risk attitudes in the laboratory. In addition to our own experimental evidence, we take a second look at the extant laboratory experiments that measure higher order risk preferences and we find a fair amount of support for this dichotomy. Our own experiment also is the first to look beyond fourth-order risk preferences, and we examine risk attitudes at even higher orders.