This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE

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Prospect theory: an analysis of decision under risk

The psychological principles that govern the perception of decision problems and the evaluation of probabilities and outcomes produce predictable shifts of preference when the same problem is framed in different ways. Reversals of preference are demonstrated in choices regarding monetary outcomes, both hypothetical and real, and in questions pertaining to the loss of human lives. The effects of frames on preferences are compared to the effects of perspectives on perceptual appearance. The dependence of preferences on the formulation of decision problems is a significant concern for the theory of rational choice.

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The Framing of Decisions and the Psychology of Choice

Publisher Summary This chapter discusses the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish. It presents alternative and more transparent proofs under these more general market conditions for Tobin's important separation theorem that “ … the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance … and for risk avertere in purely competitive markets when utility functions are quadratic or rates of return are multivariate normal. The chapter focuses on the set of risk assets held in risk averters' portfolios. It discusses various significant equilibrium properties within the risk asset portfolio. The chapter considers a few implications of the results for the normative aspects of the capital budgeting decisions of a company whose stock is traded in the market. It explores the complications introduced by institutional limits on amounts that either individuals or corporations may borrow at given rates, by rising costs of borrowed funds, and certain other real world complications.

The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets

This paper develops a theory of financial intermediation based on minimizing the cost of monitoring information which is useful for resolving incentive problems between borrowers and lenders. It presents a characterization of the costs of providing incentives for delegated monitoring by a financial intermediary. Diversification within an intermediary serves to reduce these costs, even in a risk neutral economy. The paper presents some more general analysis of the effect of diversification on resolving incentive problems. In the environment assumed in the model, debt contracts with costly bankruptcy are shown to be optimal. The analysis has implications for the portfolio structure and capital structure of intermediaries.

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Financial Intermediation and Delegated Monitoring

This book presents the definitive exposition of 'prospect theory', a compelling alternative to the classical utility theory of choice. Building on the 1982 volume, Judgement Under Uncertainty, this book brings together seminal papers on prospect theory from economists, decision theorists, and psychologists, including the work of the late Amos Tversky, whose contributions are collected here for the first time. While remaining within a rational choice framework, prospect theory delivers more accurate, empirically verified predictions in key test cases, as well as helping to explain many complex, real-world puzzles. In this volume, it is brought to bear on phenomena as diverse as the principles of legal compensation, the equity premium puzzle in financial markets, and the number of hours that New York cab drivers choose to drive on rainy days. Theoretically elegant and empirically robust, this volume shows how prospect theory has matured into a new science of decision making.

Choices, Values, and Frames

This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.

Risk Aversion in the Small and in the Large

Risk aversion in the small and in the large

Eight essays address the inherent problems of the agency relationship, such as monitoring performance and the careful design of incentives. By applying agency theory to actual practices in areas as diverse as tax-sheltered programs and transfer pricing, the contributors present conceptual tools and practical ideas for shaping agency structures to serve the best interests of both parties. A research colloquium book.

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Principals and Agents: The Structure of Business

The Bayesian revolution in statistics -- where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine -- is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the authors develop the intertwining concepts of subjective probability and utility. They then systematically and comprehensively examine the Bernoulli, Poisson, and Normal (univariate and multivariate) data generating processes. For each process they consider how prior judgments about the uncertain parameters of the process are modified given the results of statistical sampling, and they investigate typical decision problems in which the main sources of uncertainty are the population parameters. They also discuss the value of sampling information and optimal sample sizes given sampling costs and the economics of the terminal decision problems. Unlike most introductory texts in statistics, Introduction to Statistical Decision Theory integrates statistical inference with decision making and discusses real-world actions involving economic payoffs and risks. After developing the rationale and demonstrating the power and relevance of the subjective, decision approach, the text also examines and critiques the limitations of the objective, classical approach.

http://www.gbv.de/dms/ilmenau/toc/151985057.PDF

Introduction to Statistical Decision Theory

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.

John W. Pratt

Papers

Risk Aversion in the Small and in the Large

Risk aversion in the small and in the large

Principals and Agents: The Structure of Business

Introduction to Statistical Decision Theory

Risk vulnerability and the tempering effect of background risk