Exact arbitrage, well-diversified portfolios and asset pricing in large markets

Journal of Economic Theory

Volumn 110, Issue 2, 2003, Pages 337-373

  Khan, M Ali ^a   Sun, Yeneng ^b  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Arbitrage pricing theory; Asymptotic arbitrage; Essential risk; Exact arbitrage; Exact law of numbers; Loeb measure space; Well diversified portfolio

Indexed keywords

EID: 0038348025     PISSN: 00220531     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0531(03)00038-3     Document Type: Article

References (45)

1. N.I. Al-Najjar, Factor analysis and arbitrage pricing in large economies, J. Econom. Theory 78 (1998) 231-262.
2. R.M. Anderson, Non-standard analysis with applications to economics, in: W. Hildenbrand, H. Sonnenschein (Eds.), Handbook of Mathematical Economics, North-Holland Publishing Company, New York, 1991.
3. R. Ash, Information Theory, Dover Publications, Inc, New York, 1965.
4. A. Basilevsky, Statistical Factor Analysis and Related Methods, Wiley, New York, 1994.
5. T.F. Bewley, Existence of equilibria in economies with infinitely many commodities, J. Econom. Theory 4 (1972) 514-540.
6. G. Chamberlain, Funds, factors and diversification in arbitrage pricing models, Econometrica 51 (1983) 1305-1323.
7. G. Chamberlain, M. Rothschild, Arbitrage, factor structure, and mean-variance analysis on large markets, Econometrica 51 (1983) 1281-1304.
8. J.L. Doob, Stochastic processes depending on a continuous parameter, Trans. Amer. Math. Soc. 42 (1937) 107-140.
9. J.L. Doob, Stochastic Processes, Wiley, New York, 1953.
10. P. Dybvig, S.A. Ross, Arbitrage, in: J. Eatwell, P.K. Newman, M. Milgate (Eds.), The New Palgrave, MacMillan Publishing Company, London, 1987.
11. D. Duffie, Security Markets, Academic Press Inc., New York, 1988.
12. D. Duffie, Dynamic Asset Pricing Theory, Princeton University Press, Princeton, NJ, 1992.
13. M. Feldman, C. Gilles, An expository note on individual risk without aggregate uncertainty, J. Econom. Theory 35 (1985) 26-32.
14. K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd Edition, Academic Press, New York, 1990.
15. H.H. Harman, Modern Factor Analysis, 2nd Edition, University of Chicago Press, Chicago, 1968.
16. H.G. Heuser, Functional Analysis, Wiley, New York, 1982.
17. W. Hildenbrand, Core and Equilibria of a Large Economy, Princeton University Press, Princeton, NJ, 1974.
18. G. Huberman, A simple approach to arbitrage pricing theory, J. Econom. Theory 28 (1982) 183-191.
19. G. Huberman, Arbitrage pricing theory, in: J. Eatwell, P.K. Newman, M. Milgate (Eds.), The New Palgrave, MacMillan Publishing Company, London, 1987.
20. A.E. Hurd, P.A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, Orlando, 1985.
21. K.L. Judd, The law of large numbers with a continuum of iid random variables, J. Econom. Theory 35 (1985) 19-25.
22. M. Ali Khan, Y.N. Sun, Hyperfinite asset pricing theory, Cowles Foundation Discussion Paper No. 1139, 1996.
23. M. Ali Khan, Y.N. Sun, The capital-asset-pricing model and arbitrage pricing theory: a unification, Proc. Nat. Acad. Sci. USA 94 (1997) 4229-4232.
24. M. Ali Khan, Y.N. Sun, Weak measurability and characterizations of risk, Econom. Theory 13 (1999) 441-460.
25. M. Ali Khan, Y.N. Sun, Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures, J. Econom. Theory 101 (2001) 222-251.
26. M. Kurz, M. Majumdar, Efficiency prices in infinite dimensional spaces: a synthesis, Rev. Econom. Stud. 39 (1972) 147-158.
27. H.J. Keisler, Infinitesimals in probability theory, in: N. Cutland (Ed.), Nonstandard Analysis and its Applications, Cambridge University Press, New York, 1988, pp. 106-139.
28. J. Lintner, The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets, Rev. Econom. Statist. 47 (1965) 13-37.
29. P.A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975) 113-122.
30. M. Loéve, Probability Theory I, 4th Edition, Springer, New York, 1977.
31. M. Loéve, Probability Theory II, 4th Edition, Springer, New York, 1977.
32. E. Oja, Subspace Methods of Pattern Recognition, Wiley, New York, 1983.
33. R.C. Radcliffe, Investment: Concepts, Analysis, Strategy, 5th Edition, Addison-Wesley, Reading, MA, 1997.
34. H. Reisman, A general approach to the arbitrage pricing theory (APT), Econometrica 56 (1988) 473-476.
35. S.A. Ross, The arbitrage theory of capital asset pricing, J. Econom. Theory 13 (1976) 341-360.
36. S.A. Ross, Return, risk and arbitrage, in: I. Friend, J.L. Bicksler (Eds.), Risk and Return in Finance, Balinger Publishing Co., Cambridge, 1977.
37. S.A. Ross, R.W. Westerfield, J. Jaffe, Corporate Finance, 4th Edition, Irwin, Chicago, 1996.
38. M. Rothschild, Asset pricing theories, in: W.P. Heller, R.M. Starr, D. Starett (Eds.), Uncertainty, Information and Communication: Essays in honor of K.J. Arrow, Cambridge University Press, Cambridge, 1992.
39. W. Rudin, Real and Complex Analysis, McGraw-Hill Book Co., New York, 1974.
40. W. Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk, J. Finance 33 (1964) 885-901.
41. Y.N. Sun, Hyperfinite law of large numbers, Bull. Symbolic Logic 2 (1996) 189-198.
42. Y.N. Sun, A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN, J. Math. Econom. 29 (1998) 419-503.
43. Y.N. Sun, The almost equivalence of pairwise and mutual independence and the duality with exchangeability, Probab. Theory Related Fields 112 (1998) 425-456.
44. Y.N. Sun, On the sample measurability problem in modeling individual risks, Research Paper No. 99-25, Center for Financial Engineering, National University of Singapore.
45. J. Werner, Diversification and equilibrium in securities markets, J. Econom. Theory 75 (1997) 89-103.