We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986). The key elements of this theory are 1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains,

http://psych.fullerton.edu/mbirnbaum/psych466/articles/Tversky_Kahneman_JRU_92.pdf

Advances in prospect theory: cumulative representation of uncertainty

Expectations and the neutrality of money

This paper develops a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries An important feature of these general preferences is that they permit risk attitudes to be disentangled from the degree of intertemporal substitutability Moreover, in an infinite horizon, representative agent context these preference specifications lead to a model of asset returns in which appropriate versions of both the atemporal CAPM and the intertemporal consumption-CAPM are nested as special cases In our general model, systematic risk of an asset is determined by covariance with both the return to the market portfolio and consumption growth, while in each of the existing models only one of these factors plays a role This result is achieved despite the homotheticity of preferences and the separability of consumption and portfolio decisions Two other auxiliary analytical contributions which are of independent interest are the proofs of (i) the existence of recursive intertemporal utility functions, and (ii) the existence of optima to corresponding optimization problems In proving (i), it is necessary to define a suitable domain for utility functions This is achieved by extending the formulation of the space of temporal lotteries in Kreps and Porteus (1978) to an infinite horizon framework A final contribution is the integration into a temporal setting of a broad class of atemporal non-expected utility theories For homogeneous members of the class due to Chew (1985) and Dekel (1986), the corresponding intertemporal asset pricing model is derived

Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework

Much research in the last two decades has demon- strated that human responses deviate from the performance deemed normative according to various models of decision mak- ing and rational judgment (e.g., the basic axioms of utility theory). This gap between the normative and the descriptive can be inter- preted as indicating systematic irrationalities in human cognition. However, four alternative interpretations preserve the assumption that human behavior and cognition is largely rational. These posit that the gap is due to (1) performance errors, (2) computational limitations, (3) the wrong norm being applied by the experi- menter, and (4) a different construal of the task by the subject. In the debates about the viability of these alternative explanations, attention has been focused too narrowly on the modal response. In a series of experiments involving most of the classic tasks in the heuristics and biases literature, we have examined the implica- tions of individual differences in performance for each of the four explanations of the normative/descriptive gap. Performance er- rors are a minor factor in the gap; computational limitations un- derlie non-normative responding on several tasks, particularly those that involve some type of cognitive decontextualization. Un- expected patterns of covariance can suggest when the wrong norm is being applied to a task or when an alternative construal of the task should be considered appropriate.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X00003435

Individual differences in reasoning: Implications for the rationality debate?

Uncertain lifetime, life insurance, and the theory of the consumer

IN THIS ESSAY, a new theory of choice under risk is being proposed. It is a theory which, in a sense that will become clear, is dual to expected utility theory, hence the title "dual theory." Risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility, except that the roles of payments and probabilities are reversed. This theme-the reversal of the roles of probabilities and payments-will recur throughout the paper. I should emphasize that playing games, with probabilities masquerading as payments and payments masquerading as probabilities, is not my object. Rather, I hope to convince the reader that the dual theory has intrinsic economic significance and that, in some areas, its predictions are superior to those of expected utility theory (while in other areas the reverse will be the case). Two reasons have prompted me to look for an alternative to expected utility theory. The first reason is methodological: In expected utility theory, the agent's attitude towards risk and the agent's attitude towards wealth are forever bonded together. At the level of fundamental principles, risk aversion and diminishing marginal utility of wealth, which are synonymous under expected utility theory, are horses of different colors. The former expresses an attitute towards risk (increased uncertainty hurts) while the latter expresses an attitude towards wealth (the loss of a sheep hurts more when the agent is poor than when the agent is rich). A question arises, therefore, as to whether these two notions can be kept separate from each other in a full-fledged theory of cardinal utility. The dual theory will have this property. The second reason that leads me to look for an alternative to expected utility theory is empirical: Behavior patterns which are systematic, yet inconsistent with expected utility theory, have often been observed. (Two prominent references, among many others, are Allais (1953) and Kahneman-Tversky (1979).) So deeply

The Dual Theory of Choice under Risk.

We analyze in this paper a completely aggregated model of production in which output is produced by inputs of homogeneous labor and heterogeneous capital goods, and allocated either to consumption or to use as capital goods. Allocations are irreversible: capital goods can never be directly consumed. Fixed coefficients rule: any concrete unit of capital has a given output capacity and requires a given complement of labor. Technological progress continuously differentiates new capital goods from old. But we assume that the “ latest model ” in capital goods has no smaller capacity and no higher labor requirement than any older-model capital goods with the same reproduction cost. Thus each instant’s gross investment will take the form of the latest-model capital. There is no problem of the optimal “ depth ” of capital. The main effect of an increase in gross investment is to modernize the capital stock in use.

Neoclassical Growth with Fixed Factor Proportions

On the Consumer's Lifetime Allocation Process

/pdf/on-the-consumer-s-lifetime-allocation-process-1m4pjf90ee.pdf

Menahem E. Yaari

Papers

Uncertain lifetime, life insurance, and the theory of the consumer

The Dual Theory of Choice under Risk.

Neoclassical Growth with Fixed Factor Proportions

On the Consumer's Lifetime Allocation Process

On the consumer's lifetime allocation process