One theory for two different risk premia (original) (raw)

Risk-aversion concepts in expected- and non-expected-utility models

Insurance: Mathematics and Economics, 1996

The non-expected-utility tbeories of decision under risk have fovond the appearance of new notions of incieasing risk like ntonotone increasing risk (based on the notion of comonotonic random vahablcs) or new notions of risk aversion like averaion to monotone increasing risk, in better agreement witb tbese new theories. After a survey of atl tbc possible notions of increasing risk and of risk aversion and tbeir intrinsic de^nitions, we show tbat cODtivy to expected-utility tbeory where all the notions of risk avenion bave the same characterization (u concave), in the ftunework of rank-dependent expected utility (one of the most well known of the non-expectedutility models), tbe characterizations of all these notions of risk aversion are different. Moreover, we sbow tbat, even in tbe expected-utility framcworic, the new notion of monotone increasing risk can give better answers to some pn^lems of comparative sutics sucb as in ponfoUo cboice or in partial insurance. This new notion also can suggest more intuitive approaches to inequalities measurement.

1SUBSTITUTION and Risk Aversion: Is Risk Aversion Important for Understanding Asset PRICES?1

2005

The log utility function is widely used to explain asset prices. It assumes that both the elasticity of substitution and relative risk aversion are equal to one. Here I show that much of the same predictions about asset prices can be derived from a time-non-separable expected utility function that assumes an elasticity of substitution close to unity but does not impose restrictions on risk aversion to bets in terms of money. 1 I would like to thank Jeff Campbell and Greg Huffman for useful comments on an earlier draft.

Properties of the utility function: A market-based analysis

Journal of Economics and Business, 2009

Using US market data, this paper sheds new empirical light on properties of the utility function. In particular, employing theoretical relations between Stochastic Discount Factors, state prices, and state probabilities, we are successful in recovering the following four functions: (i) Absolute Risk Aversion (ARA); (ii) Absolute Risk Tolerance (ART); (iii) Absolute Prudence (AP); and (iv) Absolute Temperance (AT). Our statistical analysis points out, unequivocally, that the ARA function is decreasing and convex, the ART function is convex, AT is greater than ARA, and the AP function is not decreasing. These empirical results are analyzed in light of established theory concerning, inter-alia, precautionary saving and prudence as well as the way risk attitudes are affected by the presence of "background risks" and by investors' investment horizon. discuss the recoverability of preferences from observed asset prices and an agent's consumption choice. Jackwerth is the first to use estimates of state prices and physical probabilities to recover A RA functions. We extend on that by characterizing additional properties of the vNM utility function, and relying on a more general approach for estimating state probabilities. Our approach is shown to have non-trivial consequences.

Valuing Bets and Hedges: Implications for the Construct of Risk Preference

Behavioral & Experimental Finance eJournal, 2018

Risk attitudes implied by valuations of risk-increasing assets depart markedly from those implied by valuations of risk-reducing assets. For instance, many are unwilling to pay the expected value for a risky asset or for its perfect hedge. Although nearly every theory of risk preference (and logic) demands a negative correlation between valuations of bets and hedges, we observe positive correlations. This inconsistency is difficult to expunge.

Non-expected utility risk premiums: The cases of probability ambiguity and outcome uncertainty

Journal of Risk and Uncertainty, 1988

This paper discusses two problems. (a) What happens to the conditional risk premium that a decision maker is willing to pay out of the middle prize in a lottery to avoid uncertainty concerning the middle prize outcome, when the probabilities of other prizes change? (b) What happens to the increase that a decision maker is willing to accept in the probability of an unpleasant outcome in order to avoid ambiguity concerning this probability, when this probability increases? We discuss both problems by using anticipated utility theory, and show that the same conditions on this functional predict behavioral patterns that are consistent both with a natural extension of the concept of diminishing risk aversion and with some experimental findings.

Alternative Models of Risk Behavior

Risk Analysis in Theory and Practice, 2004

The expected utility model provides the basis for most of the research on the economics of risk. It was the topic presented in Chapter 3. Under the expected utility model, individuals make decisions among alternative wealth levels x by maximizing EU(x) where E is the expectation operator. The utility function U(x) is defined up to a positive linear transformation. It is sometimes called a von Neumann-Morgenstern utility function. We saw in Chapter 4 that risk aversion, risk neutrality, or risk loving preferences correspond to the function U(x) being respectively concave, linear, or convex. One of the main advantages of the expected utility model is its empirical tractability. This is the reason why it is commonly used in risk analysis. But is the expected utility model a good predictor of human behavior? Sometimes, it is. And sometimes, it is not. This chapter evaluates some of the evidence against the expected utility model. It also reviews alternative models that have been proposed to explain behavior under risk. The first challenge to the expected utility model is the following: Is it consistent with the fact that some individuals both insure and gamble at the same time? Friedman and Savage proposed to explain this by arguing that, for most individuals, the utility function U(x) is probably concave (corresponding to risk aversion and a positive willingness to insure) for low or moderate monetary rewards, but convex (corresponding to risk loving and a positive willingness to gamble) for high monetary rewards. In this context, a particular individual can insure against ''downside risk'' while at the same time gambling on ''upside risk'' and still be consistent with the expected utility model.

Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions

Research Papers in Economics, 2018

The Diffidence Theorem, together with complementary tools, can aid in illuminating a broad set of questions about how to mathematically characterize the set of utility functions with specified economic properties. This paper establishes the technique and illustrates its application to many questions, old and new. For example, among many other older and other technically more difficult results, it is shown that (1) several implications of globally greater risk aversion depend on distinct mathematical properties when the initial wealth level is known, (2) whether opening up a new asset market increases or decreases saving depends on whether the reciprocal of marginal utility is concave or convex, and (3) whether opening up a new asset market raises or lowers risk aversion towards small independent risks depends on whether absolute risk aversion is convex or concave.