Abstract
Classic formulations of markets regard uncertainty as originating from acts of nature. I extend this to a formulation of markets which face risks induced by the economy itself, such as the environmental risks of atmospheric and climate change induced by CFC and CO2 emissions.
I formulate and prove the existence of a general competitive equilibrium where the state space and the probabilities of events are endogenously determined as part of the equilibrium. Traders take optimal positions with respect to the uncertainty which their own actions induce. The equilibrium allocations are efficient in a restricted sense. I show that scientific uncertainty can be fully hedged. However uncertainty induced by the unknown level of output at an equilibrium cannot be hedged fully. I discuss applications for CAT Futures, recently introduced on the Chicago Board of Trade, and to international environmental strategies.
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Arrow, K.J.: 1953, ‘The role of securities in the optimal allocation of risk-bearing’, in French:Econometric: Proceedings of the Colloque sur les Fondments et Applications de la Theorie du Risque en Econometrie, Centre National de la Recherche Scientifique, Paris. English Translation:Review of Economic Studies (1964)31: 91–96.
Arrow, K.J.: 1963, ‘Uncertainty and the Welfare Economics of Medical Care’,American Economic Review LIII(5), 941–973.
Berger, Melvyn S.: 1977,Nonlinearity and Functional Analysis, Lectures on Nonlinear Problems in Mathematical Analysis. Academic Press, New York, San Francisco, London.
Cass, D.G. Chichilnisky, and H-M Wu: 1996, ‘Individual Risks and Mutual Insurance’,Econometrica 64(2), 333–342.
Chichilnisky, G.: 1977, ‘Spaces of Economic Agents’,Journal of Economic Theory 15(1), pp. 106–73.
Chichilnisky, G.: 1992, ‘Existence and Optimality of a Competitive Equilibrium with Endogenous Uncertainty’, Working Paper, Columbia University, December 1992.
Chichilnisky, G.: 1993, ‘Comment: The Taxation of Carbon Emissions in Industrial and Developing Countries’, inOECD: The Economies of Climate Change (ed. T. Jones), Paris, 1994, pp. 159–170.
Chichilnisky, G.: 1993, ‘Social Diversity, Arbitrage and Gains from Trade: A Unified Perspective on Resource Allocation’,American Economic Review, May 1994, 427–433.
Chichilnisky, G.: 1991, ‘Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium With or Without Short Sales’, Working Paper, Columbia University,Economic Theory, January 1995, Vol 5, No 1, pp. 79–108.
Chichilnisky, G.: 1994, ‘A Unified Perspective on Resource Allocation: Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium, the Core and Social Choice’, Invited Presentation at the International Economic Association (IEA) Round Table on Social Choice, Schloss Hernstein, Austria, May 25–28, 1994, forthcoming inSocial Choice Reexamined (ed. K. Arrow, A. Sen and K. Suzumura), MacMillan.
Chichilnisky, G.: 1994, ‘Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium and the Core, and Limits Voting Cycles’,Economic Letters,46, pp. 321–331, to reappear as “Limited Arbitrage is Necessary and Sufficient for the Nonemptiness of the Core”,Economic Letters, 1996.
Chichilnisky, G., and G.M. Heal: 1993, ‘The Existence and Structure of the Pseudoequilibrium Manifold in Incomplete Asset Markets’, forthcoming,Journal of Mathematical Economics, 1996.
Chichilnisky, G. and G.M. Heal: 1992, ‘Global Environmental Risks’,Journal of Economic Perspectives,7(4), pp. 65–86.
Chichilnisky, G. and G.M. Heal: 1993, ‘Existence of a Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales’,Journal of Economic Theory,59(2) pp. 364–384.
Chichilnisky, G. and G.M. Heal: 1992, ‘Financial Markets with Unknown Risks’, Working Paper, Columbia University.
Chichilnisky, G. and H.-M. Wu.: 1991, ‘Financial Innovation and Endogenous Default in Incomplete Asset Markets’, Stanford Institute for Theoretical Economics Technical Report No. 50, 1992, forthcoming inInformation and Uncertainty: New Directions in Economic Theory, Essays in Honor of Kenneth Arrow (ed. G. Chichilnisky), Cambridge University Press.
Chichilnisky, G., J. Dutta, G.M. Heal: 1991, ‘Price Uncertainty and Derivative Securities in General Equilibrium’, Working Paper, Columbia University, revised 1993.
Chichilnisky, G., G.F. Hahn and G.M. Heal: 1992, ‘Price Uncertainty and Incomplete Markets’, Working Paper, Columbia Business School.
Chichilnisky, G., G.M. Heal, P. Streufert, and J. Swinkels: 1992, ‘Believing in Multiple Equilibrium’, Stanford Institute for Theoretical Economics Technical Report No. 49, August 1992, and First Boston Working Paper FB-92-32, Columbia Business School, August 1992.
Chichilnisky, G., G.M. Heal, and D. Tsomocos: 1994, ‘Option Values and Endogenous Uncertainty in ESOP's, MBO's and Asset Backed Securities’, Working Paper, Columbia Business School and Yale University,Economic Letters, 1995, Vol 48. No 3–4, pp. 379–388.
Dasgupta, P. and G.M. Heal: 1979,Economic Theory and Exhaustible Resources, Cambridge University Press.
Eaves, C.: 1972, ‘Homotopies for Computation of Fixed Points’,Math. Programming 3.
Fudenberg, D.B. Holstrom and P. Milgrom: 1990, ‘Short-term Contracts and Long-term Agency Relationships’,Journal of Economic Theory,51(1), June 1990.
Hahn, F.: 1991, ‘A Remark on Incomplete Market Equilibrium’, Working Paper Cambridge University and University of Siena, to appear inInformation and Uncertainty: New Directions in Economic Theory, Essays in Honor of Kenneth Arrow (ed. G. Chichilnisky), Cambridge University Press.
Hahn, F.: 1992, ‘Making General Equilibrium Theory More Plausible’,The Second Annual Arrow Lecture Series, Department of Economics, Stanford University, May 5 and 6.
Hahn, F.: 1973,The Concept of Equilibrium in Economics, Inaugural Lecture, Cambridge University, Cambridge University Press.
Heal, G.: 1984, ‘Interaction of the Economy and Climate: A Framework for Policy Design under Uncertainty’ in Smith, Kerry and Ann Dryden White eds.Advances in Applied Macroeconomics, Greenwich, J.A.I. Press, 151–158.
Heal, G.M.: 1990, ‘Economy and Climate: A Preliminary Framework for Microeconomic Analysis’, in Just, Richard and Nancy Bockstael, eds.Commodity and Natural Resource Policies in Agricultural Systems, New York and Oxford: North Holland 1993, 855–880.
Kurz, M.: 1974, ‘The Kesten-Stigum Model and the Treatment of Uncertainty in Equilibrium Theory’, in M.C. Balch, D.McFadden, and S. Wu, (eds.)Essays in Economic Behavior Under Uncertainty, North Holland.
Kurz, M.: 1991, ‘On the Structure and Diversity of Rational Beliefs’, Technical Report No. 31, Stanford Institute of Theoretical Economics,Economic Theory, 1994.
Milnor, J.: 1965,Topology from a Differentiable Viewpoint, The University Press of Virginia, Charlottesville.
Stiglitz, J.: 1974, ‘Tax Policy and the Oil Industry’, mimeo, Yale University.
Stiglitz, J.: 1983, ‘Risk Incentives and Insurance: The Pure Theory of Moral Hazard’,The Geneva Papers, January 1983, 8:26. 4–32.
Stein, J.: 1992, ‘Cobwebs, Rational Expectations and Futures Markets’,Review of Economics and Statistics,LXXIV(1), pp. 127–134.
Stein, J.: 1992, ‘Price Discovery Processes’,Economic Record, pp. 34–45.
Wilson, Robert: 1992, ‘Strategic Analysis of Auctions’,Handbook of Game Theory, Vol. 1 (R. Aumann and S. Hart eds.), Elsevier Science Publishers, B.V.
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Dedicated to Tjalling C. Koopmans
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Chichilnisky, G. Markets with endogenous uncertainty theory and policy. Theor Decis 41, 99–131 (1996). https://doi.org/10.1007/BF00134638
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DOI: https://doi.org/10.1007/BF00134638