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Risk

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Abstract

The phenomenon of risk plays a pervasive role in economics. Without it, financial and capital markets would consist of the exchange of a single instrument each period, the communications industry would cease to exist, and the profession of investment banking would reduce to simple accounting. One need but consult the contents of any recent economics journal to see how the recognition of risk has influenced current research in the discipline. This article presents an overview of the modern economic theory of the characterization of risk and the modelling of economic agents’ responses to it.

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Bibliography

  • Anscombe, F., and R. Aumann. 1963. A definition of subjective probability. Annals of Mathematical Statistics 34: 199–205.

    Article  Google Scholar 

  • Arrow, K. 1964. The role of securities in the optimal allocation of risk-bearing. Review of Economic Studies 31: 91–96.

    Article  Google Scholar 

  • Baker, E. 2006. Increasing risk and increasing informativeness: Equivalence theorems. Operations Research 54: 26–36.

    Article  Google Scholar 

  • Bawa, V. 1982. Stochastic dominance: A research bibliography. Management Science 28: 698–712.

    Article  Google Scholar 

  • Beladi, H., L. de la Vina, and F. Firoozi. 2006. On information value and mean-preserving transformations. Applied Mathematics Letters 19: 843–848.

    Article  Google Scholar 

  • Borch, K. 1969. A note on uncertainty and indifference curves. Review of Economic Studies 36: 1–4.

    Article  Google Scholar 

  • Chateauneuf, A., M. Cohen, and I. Meilijson. 2004. Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model. Journal of Mathematical Economics 40: 547–571.

    Article  Google Scholar 

  • Debreu, G. 1959. Theory of value: An axiomatic analysis of general equilibrium. New Haven: Yale University Press.

    Google Scholar 

  • Diamond, P., and M. Rothschild, eds. 1989. Uncertainty in economics: Readings and exercises. 2nd ed. New York: Academic.

    Google Scholar 

  • Diamond, P., and J. Stiglitz. 1974. Increases in risk and in risk aversion. Journal of Economic Theory 8: 337–360.

    Article  Google Scholar 

  • Dionne, G., L. Eeckhoudt, and C. Gollier. 1993. Increases in risk and linear payoffs. International Economic Review 34: 309–319.

    Article  Google Scholar 

  • Eeckhoudt, L., C. Gollier, and H. Schlesinger. 1996. Changes in background risk and risk taking behavior. Econometrica 64: 683–689.

    Article  Google Scholar 

  • Ekern, S. 1980. Increasing nth degree risk. Economics Letters 6: 329–333.

    Article  Google Scholar 

  • Epstein, L., and S. Tanny. 1980. Increasing generalized correlation: A definition and some economic consequences. Canadian Journal of Economics 13: 16–34.

    Article  Google Scholar 

  • Feldstein, M. 1969. Mean-variance analysis in the theory of liquidity preference and portfolio selection. Review of Economic Studies 36: 5–12.

    Article  Google Scholar 

  • Fishburn, P. 1982. Simplest cases of n’th degree stochastic dominance. Operations Research Letters 1: 89–90.

    Article  Google Scholar 

  • Fishburn, P. and Vickson, R. 1978. Theoretical foundations of stochastic dominance, in Whitmore and Findlay (1978).

    Google Scholar 

  • Gärdenfors, P., and N.-E. Sahlin, eds. 1988. Decision, probability, and utility: Selected readings. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hadar, J., and W. Russell. 1969. Rules for ordering uncertain prospects. American Economic Review 59: 25–34.

    Google Scholar 

  • Hanoch, G., and H. Levy. 1969. The efficiency analysis of choices involving risk. Review of Economic Studies 36: 335–346.

    Article  Google Scholar 

  • Hansen, L., C. Holt, and D. Peled. 1978. A note on first degree stochastic dominance. Economics Letters 1: 315–319.

    Article  Google Scholar 

  • Hey, J., ed. 1997. The economics of uncertainty, vol. II: Uncertainty and dynamics. Cheltenham: Edward Elgar.

    Google Scholar 

  • Hicks, J. 1962. Liquidity. Economic Journal 72: 787–802.

    Article  Google Scholar 

  • Hirshleifer, J. 1965. Investment decision under uncertainty: Choice-theoretic approaches. Quarterly Journal of Economics 79: 509–536.

    Article  Google Scholar 

  • Hirshleifer, J. 1966. Investment decision under uncertainty: Applications of the state- preference approach. Quarterly Journal of Economics 80: 252–277.

    Article  Google Scholar 

  • Huang, C., D. Kira, and I. Vertinsky. 1978. Stochastic dominance for multi-attribute utility functions. Review of Economic Studies 45: 611–616.

    Article  Google Scholar 

  • Jewitt, I. 1987. Risk aversion and the choice between risky prospects: The preservation of comparative statics results. Review of Economic Studies 54: 73–85.

    Article  Google Scholar 

  • Karni, E. 1985. Decision making under uncertainty: The case of state dependent preferences. Cambridge, MA: Harvard University Press.

    Book  Google Scholar 

  • Knight, F. 1921. Risk, uncertainty and profit. Boston: Houghton Mifflin.

    Google Scholar 

  • Kyberg, H., and H. Smokler, eds. 1964. Studies in subjective probability. New York: Wiley.

    Google Scholar 

  • Lehmann, E. 1955. Ordered families of distributions. Annals of Mathematical Statistics 26: 399–419.

    Article  Google Scholar 

  • Levhari, D., J. Paroush, and B. Peleg. 1975. Efficiency analysis for multivariate distributions. Review of Economic Studies 42: 87–91.

    Article  Google Scholar 

  • Levy, H., and J. Paroush. 1974. Toward multivariate efficiency criteria. Journal of Economic Theory 7: 129–142.

    Article  Google Scholar 

  • Lintner, J. 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 44: 243–269.

    Article  Google Scholar 

  • Machina, M., and J. Pratt. 1997. Increasing risk: Some direct constructions. Journal of Risk and Uncertainty 14: 103–127.

    Article  Google Scholar 

  • Machina, M., and D. Schmeidler. 1992. A more robust definition of subjective probability. Econometrica 60: 745–780. Reprinted in Hey (1997).

    Article  Google Scholar 

  • Markowitz, H. 1952. Portfolio selection. Journal of Finance 7: 77–91.

    Google Scholar 

  • Markowitz, H. 1959. Portfolio selection: Efficient diversification of investment. New Haven: Yale University Press.

    Google Scholar 

  • Marshall, A., and I. Okun. 1979. Inequalities: Theory of majorization and its applications. New York: Academic.

    Google Scholar 

  • Meyer, J. 1987. Two-moment decision models and expected utility maximization. American Economic Review 77: 421–430.

    Google Scholar 

  • Mossin, J. 1966. Equilibrium in a capital asset market. Econometrica 34: 768–783.

    Article  Google Scholar 

  • Nowak, M. 2004. Interactive approach in multicriteria analysis based on stochastic dominance. Control and Cybernetics 33: 463–476.

    Google Scholar 

  • Ormiston, M. 1992. First and second degree transformations and comparative statics under uncertainty. International Economic Review 33: 33–44.

    Article  Google Scholar 

  • Pratt, J. 1964. Risk aversion in the small and in the large. Econometrica 32: 122–136. Reprinted in Diamond and Rothschild (1989).

    Article  Google Scholar 

  • Pratt, J., H. Raiffa, and R. Schlaifer. 1964. The foundations of decision under uncertainty: An elementary exposition. Journal of the American Statistical Association 59: 353–375.

    Article  Google Scholar 

  • Raiffa, H. 1968. Decision analysis: Introductory lectures on choice under uncertainty. Reading: Addison Wesley.

    Google Scholar 

  • Ramsey, F. 1926. Truth and probability. In The foundations of mathematics and other logical essays, ed. R.B. Braithwaite. London: Routledge & Kegan Paul. 1931. Reprinted in Kyberg and Smokler (1964), Ramsey (1978), and Gärdenfors and Sahlin (1988).

    Google Scholar 

  • Ramsey, F. 1978. In Foundations: Essays in philosophy, mathematics and economics, ed. D.H. Mellor. London: Routledge & Kegan Paul.

    Google Scholar 

  • Rothschild, M., and J. Stiglitz. 1970. Increasing risk: I. A definition. Journal of Economic Theory 2: 225–243. Reprinted in Diamond and Rothschild (1989).

    Article  Google Scholar 

  • Rothschild, M., and J. Stiglitz. 1971. Increasing risk: II. Its economic consequences. Journal of Economic Theory 3: 66–84.

    Article  Google Scholar 

  • Rothschild, M., and J. Stiglitz. 1972. Addendum to ‘increasing risk: I. a definition’. Journal of Economic Theory 5: 306.

    Article  Google Scholar 

  • Russell, W., and T. Seo. 1978. Ordering uncertain prospects: The multivariate utility functions case. Review of Economic Studies 45: 605–611.

    Article  Google Scholar 

  • Samuelson, P. 1967. General proof that diversification pays. Journal of Financial and Quantitative Analysis 2: 1–13.

    Article  Google Scholar 

  • Savage, L. 1954. The foundations of statistics. New York: Wiley. Rev. edn, New York: Dover Publications, 1972.

    Google Scholar 

  • Sharpe, W. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19: 425–442.

    Google Scholar 

  • Sherman, S. 1951. On a theorem of Hardy, Littlewood, Polya, and Blackwell. Proceedings of the National Academy of Science 37: 826–831. Errata. Proc. Nat. Ac. Sci. 38, 382.

    Article  Google Scholar 

  • Strassen, V. 1965. The existence of probability measures with given marginals. Annals of Mathematical Statistics 36: 423–439.

    Article  Google Scholar 

  • Tesfatsion, L. 1976. Stochastic dominance and the maximization of expected utility. Review of Economic Studies 43: 301–315.

    Article  Google Scholar 

  • Tobin, J. 1958. Liquidity preference as behavior toward risk. Review of Economic Studies 25: 65–86.

    Article  Google Scholar 

  • Treynor, J. 1999. Toward a theory of market value of risky assets. In Asset Pricing and Portfolio Performance, ed. R. Korajczyk. London: Risk Books. In Korajczyk (1999).

    Google Scholar 

  • Tzeng, L. 2001. Increase in risk and weaker marginal-payoff-weighted risk dominance. The Journal of Risk and Insurance 68: 329–337.

    Article  Google Scholar 

  • Whitmore, G. 1970. Third-degree stochastic dominance. American Economic Review 60: 457–459.

    Google Scholar 

  • Whitmore, G., and M. Findlay. 1978. Stochastic dominance: An approach to decision making under risk. Lexington: Heath.

    Google Scholar 

  • Yaari, M. 1969. Some remarks on measures of risk aversion and on their uses. Journal of Economic Theory 1: 315–329. Reprinted in Diamond and Rothschild (1989).

    Article  Google Scholar 

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  1. http://link.springer.com/referencework/10.1057/978-1-349-95121-5

    Mark J. Machina & Michael Rothschild

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  1. Mark J. Machina
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  2. Michael Rothschild
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Machina, M.J., Rothschild, M. (2018). Risk. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1728

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