On equilibrium in Hart's securities exchange model |
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| Institution: | 1. Department of Chemistry and Biochemistry, University of California at Santa Barbara, Santa Barbara, CA, 93106, United States;2. Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA, 93106, United States;3. Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA, 93106, United States;4. Interdepartmental Program in Biomolecular Science and Engineering, University of California at Santa Barbara, Santa Barbara, CA, 93106, United States;1. Department of CEA, GLA University, Mathura, Uttar Pradesh, India;2. Department of Computer Information System, University of Malta, Msida, Malta;3. Department of Electronics Communication & Engineering, LNCT College, Bhopal, India;4. Department of Computer Science & Engineering, Maharaja Surajmal Institute of Technology, New Delhi, India;5. Department of Computer Science Engineering, Amity University, Gwalior, India;6. Department of Electronics Communication & Engineering, Holy Mary Institute of Technology and Science, Hyderabad, India;7. Department of Computer Science Engineering, Bhabha University, Bhopal, India;1. Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai 600036, India;2. Discipline of Metallurgy Engineering and Materials Science, Indian Institute of Technology Indore, Simrol, Khandwa Road, Indore 453552, Madhya Pradesh, India;3. Materials Chemistry, RWTH Aachen University, Aachen, Germany;1. Department of Finance, University of Melbourne, Level 12, 198 Berkeley Street, Parkville, VIC 3010, Australia\n;2. Columbia Business School, 801 Uris Hall, 3022 Broadway, New York, NY 10027, United States\n;3. University of Technology Sydney, PO Box 123 Broadway, NSW 2007, Australia;4. Stockholm School of Economics in Riga, Strelnieku Street 4a, Riga, LV 1010, Latvia |
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| Abstract: | In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations. |
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