Abstract
The concept of risk is essential to many problems in economics and business. Usually, risk is treated in the traditional expected utility framework where it is defined only indirectly through the shape of the utility function. The purpose of utility functions, however, is to model preferences. In this paper, we review those approaches which directly model risk judgements. After a short review of naive risk measures used in earlier economic literature, we present recent theoretical and empirical developments.
Zusammenfassung
Risiko ist ein Konzept, das bei der Behandlung vieler volks-oder betriebswirtschaftlicher Probleme eine wesentliche Rolle spielt. Üblicherweise wird Risiko im Rahmen des traditionellen Erwartungsnutzenmodells behandelt, bei dem es nur indirekt über die Form der Nutzenfunktion erfaßt wird. Der Zweck von Nutzenfunktionen besteht aber darin, Präferenzen zu modellieren. In diesem Aufsatz wird ein Überblick über solche Ansätze gegeben, die Risikowahrnehmungen direkt modellieren. Nach einer kurzen Darstellung naiver Risikomaße, die aus der früheren ökonomischen Literatur bekannt sind, werden neuere theoretische und empirische Konzepte präsentiert.
Similar content being viewed by others
References
Albrecht P (1993) Normal and lognormal shortfall risk. In: 3rd AFIR-Colloquium, Rome 2:417–430
Albrecht P (1996a) Zur Konzeptionalisierung von Risiko und Chance mit Anwendungen in den Finanz- und Versicherungsmärkten. In: Hübner U, Helten E, Albrecht P (eds) Recht und Ökonomie der Versicherung. Verlag Versicherungswirtschaft, Karlsruhe, pp 1–22
Albrecht P (1996b) Dimensionen des versicherungstechnischen Risikos. In: Hesberg D, Nell M, Schott W (eds) Risiko — Versicherung — Markt. Verlag Versicherungswirtschaft, Karlsruhe, pp 325–339
Allais M (1953) Le comportement de l'homme rationel devant le risque: Critique des postulats et axiomes de l'école americaine. Econometrica 21:503–546
Aschenbrenner KM (1978) Expected Risk and Single-peaked Preferences. Acta Psychologica 42:343–356
Bayerische Rück (Hrsg) (1993) Risiko ist ein Konstrukt. Knesebeck, München
Bernoulli D (1738) Specimen theoriae novae de mensura sortis. Commentarii academiae scientarum imperialis petropolitanae 5:175–192
Bernoulli D (1954) Exposition of a New Theory on the Measurement of Risk (Übersetzung von [7]). Econometrica 22:23–36
Bowman EH (1982) Risk Seeking by Troubled Firms. Sloan Management Review Summer Volume:33–42
Brachinger HW (1988) Entscheidungen bei Risiko: Kritik am Bernoulli-Paradigma und entscheidungstheoretische Fundierung des sensitivitätsanalytischen Ansatzes. Habilitationsschrift, Universität Tübingen, Tübingen, Germany
Brachinger HW (1991) Mean-Risk Decision Analysis under Partial Information. In: Chikán A (ed) Progress in Decision, Utility and Risk Theory. Kluwer Academic Publishers, Dordrecht Boston London, pp 193–201
Brachinger HW (1994) Theory of Risk under Partial Probability Information. Working Paper Nr. 241, Institute for Economic and Social Sciences, University of Fribourg, Fribourg, Switzerland
Brachinger HW (1995) Weak Lexicographic Risk-Value Models. In: Derigs U, Bachem A, Drexl A (eds) OR-Proceedings 1994. Springer, Berlin Heidelberg New York, pp 495–499
Brachinger HW (1997) Entscheidungen, Risiko und Ambiguität (überarbeitete und ergänzte Fassung von [10]). Springer, Berlin Heidelberg New York (to appear)
Brachinger HW, Schubert R (1985) The robust decision concept: An application to project evaluation. Management International Review 25:34–43
Burgemeister J, Weber M (1993) Risiko und Akzeptanz von Industrieansiedlungen. Zeitschrift für Betriebswirtschaft 63:147–169
Camerer C, Weber M (1992) Recent Developments in Modelling Preferences: Uncertainty and Ambiguity. Journal of Risk and Uncertainty 5:325–370
Colson G (1981) Toward a Bipolar Theory of Risk. European Journal of Operations Research 6:352–359
Colson G (1985) Theories of Risk and MCDM. In: Fandel G, Spronk J (eds) Multiple Criteria Decision Methods and Applications. Springer, Berlin Heidelberg New York, pp 171–196
Colson G, Zeleny M (1980) Uncertain Prospects Ranking and Portfolio Analysis under the Conditions of Partial Information. Oelgeschlager, Gunn & Hain, Cambridge MA, USA
Coombs CH (1973) The Mathematical Psychology of Risk and a Theory of Risky Decision Making. Working Paper, University of Michigan, Ann Arbor, USA
Coombs CH, Bowen JN (1971) A Test of VE-Theories of Risk and the Effect of the Central Limit Theorem. Acta Psychologica 35:15–28
Coombs CH, Huang LC (1970a) Polynominal Psychophysics of Risk. Journal of Mathematical Psychology 7:317–338
Coombs CH, Huang LC (1970b) Tests of a Portfolio Theory of Risk Preference. Journal of Experimental Psychology 85:23–39
Coombs CH, Lehner PE (1984) Conjoint Design and Analysis of the Bilinear Model: An Application to the Judgement of Risk. Journal of Mathematical Psychology 28:1–12
Coombs CH, Meyer DE (1969) Risk Preference in Coin-toss Games. Journal of Mathematical Psychology 6:514–527
Ellsberg D (1961) Risk, Ambiguity, and the Savage Axioms. Quarterly Journal of Economics 75:643–669
Fishburn PC (1977) Mean-Risk Analysis with Risk Associated with Below-Target Returns. The American Economic Review 67:116–126
Fishburn PC (1982) Foundations of Risk Measurement. II. Effects of Gains on Risk. Journal of Mathematical Psychology 25:226–242
Fishburn PC (1984) Foundations of Risk Measurement. I. Risk as Probable Loss. Management Science 30:396–406
Fishburn PC, Kochenberger GA (1979) Concepts, Theory, and Techniques: Two-Piece von Neumann-Morgenstern Utility Functions. Decision Sciences 10:503–518
Hershey JC, Schoemaker PJH (1980) Risk-Taking and Problem Context in the Domain of Losses: An Expected Utility Analysis. Journal of Risk and Insurance 47:111–132
Hershey JC, Kunreuther HC, Schoemaker PJH (1982) Sources of Bias in Assessment Procedures for Utility Functions. Management Science 28:936–954
Jia J, Dyer JS (1995) A Standard Measure of Risk and Risk-Value Models. Working Paper No. 1, Risk-Value Study Series, Department of Management Science and Information Systems, The Graduate School of Business, University of Texas at Austin, Management Science (to appear)
Kahneman D, Tversky A (1979) Prospect Theory: An Analysis of Decision Under Risk. Econometrica 47:263–291
Keller LR (1986) Twenty Years of Experiments on the Riskiness of Gambles. Working Paper, University of Irvine, Irvine, USA
Keller LR, Sarin RK, Weber M (1986) Empirical Investigation of some Properties of the Perceived Riskiness of Gambles. Organizational Behavior and Human Decision Processes 38:114–130
Knight F (1921) Risk, Uncertainty, and Profit. Boston
Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of Measurement. Academic Press, New York London
Laughhunn, DJ, Payne JW, Crum R (1980) Managerial Risk Preference for Below-Target Returns. Management Science 26:1238–1249
Luce RD (1980) Several Possible Measures of Risk. Theory and Decision 12:217–228
Luce RD (1981) Correction to: Several Possible Measures of Risk. Theory and Decision 13:381
Luce RD, Raiffa H (1957) Games and Decisions. John Wiley, New York
Luce RD, Weber EU (1986) An Axiomatic Theory of Conjoint, Expected Risk. Journal of Mathematical Psychology 30:188–205
Machina M (1982) Expected Utility Analysis without the Independence Axiom. Econometrica 50:277–323
Machina M, Rothschild M (1987) Risk. In: The New Palgrave, A Dictionary of Economics. The Macmillan Press, London
Markowitz HM (1952) Portfolio Selection. The Journal of Finance 7:77–91
Markowitz HM (1959) Portfolio Selection: Efficient Diversification of Investment. Yale University Press, New Haven, USA
Payne JW (1975) Relation of Perceived Risk to Preferences among Gambles. Journal of Experimental Psychology: Human Perception and Performance 104:86–94
Payne JW, Laughhunn DJ, Crum R (1980) Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior. Management Science 26:1039–1060
Payne JW, Laughhunn DJ, Crum R (1981) Further Tests of Aspiration Level Effects in Risky Choice Behavior. Management Science 27:953–958
Pollatsek A, Tversky A (1970) A Theory of Risk. Journal of Mathematical Psychology 7:540–553
Sarin RK (1987) Some Extensions of Luce's Measures of Risk. Theory and Decision 22:125–141
Sarin RK, Weber M (1993) Risk-Value Models. European Journal of Operations Research 70:135–149
Schneeweiss H (1967) Entscheidungskriterien bei Risiko. Springer, Berlin Heidelberg New York
Sharpe WF (1964) Capital Asset Prices: A Theory of Market Equilibrium and Conditions of Risk. Journal of Finance 19:425–442
Slovic P (1967) The Relative Influence of Probabilities and Payoffs upon Perceived Risk of a Gamble. Psychonomic Science 9:223–224
Slovic P (1987) Perception of Risk. Science 236:280–285
Stone BK (1970) Risk, Return, and Equilibrium. MIT Press, Cambridge London
Stone BK (1973) A General Class of Three-Parameter Risk Measures. Journal of Finance 28:675–685
Tobin J (1958) Liquidity Preference as a Behavior Toward Risk. Review of Economic Studies 25:65–86
Weber EU (1984a) Combine and Conquer: A Joint Application of Conjoint and Functional Approaches to the Problem of Risk Measurement. Journal of Experimental Psychology, Human Perception and Performance 10:179–194
Weber EU (1984b) Risk as an Independent Variable in Risky Choice. Doctoral Dissertation, Harvard University, Cambridge MA, USA
Weber EU (1988) A Descriptive Measure of Risk. Acta Psychologica 69:185–203
Weber EU, Bottom WP (1989) Axiomatic Measures of Perceived Risk: Some Tests and Extensions. Journal of Behavioral Decision Making 2:113–131
Weber EU, Milliman RA (1996) Perceived Risk Attitudes: Relating Risk Perception to Risky Choice. Management Science (to appear)
Weber EU, Anderson C, Birnbaum MH (1992) A Theory of Perceived Risk and Attractiveness. Organizational Behavior and Human Decision Processes 52:492–523
Weber M (1990) Risikoentscheidungskalküle in der Finanzierungstheorie. Poeschel, Stuttgart
Weber M, Camerer C (1987) Recent Developments in Modelling Preferences under Risk. OR Spektrum 9:129–151
Yates JF (1992) (ed) Risk-Taking Behavior. John Wiley, Chichester New York etc
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brachinger, H.W., Weber, M. Risk as a primitive: A survey of measures of perceived risk. OR Spektrum 19, 235–250 (1997). https://doi.org/10.1007/BF01539781
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01539781