Using Tucker's theorem of the alternative to simplify, review and expand discrete arbitrage theory

Journal of Banking and Finance

Volumn 31, Issue 8, 2007, Pages 2281-2302

  Kallio, Markku ^a   Ziemba, William T ^b,c,d  

^a HELSINKI SCHOOL OF ECONOMICS   (Finland)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c UNIVERSITY OF ZURICH   (Switzerland)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Arbitrage theory; Asset pricing; Derivatives pricing; Imperfect markets; Incomplete markets; Options pricing

Indexed keywords

EID: 34447622111     PISSN: 03784266     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbankfin.2007.02.004     Document Type: Article

References (50)

1. Arrow K. Essays in the Theory of Risk Bearing (1970), North-Holland, London
2. Bensaid B., Lesne J., Pagés H., and Scheinkman J. Derivative asset pricing with transaction costs. Mathematical Finance 2 (1992) 63-86
3. Bergman Y. Option pricing with differential interest rates. Review of Financial Studies 8 (1995) 475-500
4. Bertsimas D., Kogan L., and Lo A.W. Hedging derivative securities and incomplete markets: An ε{lunate}-arbitrage approach. Operations Research 49 (2001) 327-397
5. Boyle P., and Vorst T. Option replication in discrete time with transaction costs. Journal of Finance 47 (1992) 271-293
6. Björk T. Arbitrage Theory in Continuous Time (1998), Oxford University Press, Oxford
7. Black F., and Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 81 (1973) 637-654
8. Constantinides G. Multiperiod consumption and investment behavior with convex transaction costs. Management Science 25 (1976) 1127-1137
9. Cox J., and Ross S. The valuation of options for alternative stochastic processes. Journal of Financial Economics 3 (1976) 145-166
10. Cox J., Ross S., and Rubinstein M. Option pricing: A simplified approach. Journal of Financial Economics 7 (1979) 229-264
11. Cvitanić J., and Karatzas I. Hedging and portfolio optimization under transaction costs: A martingale approach. Mathematical Finance 6 (1996) 133-165
12. Cvitanić J. Theory of portfolio optimization in markets with frictions. In: Jouini E., Cvitanic J., and Musiela M. (Eds). Option Pricing Interest Rates and Risk Management. Handbooks in Mathematical Finance (2001), Cambridge University Press
13. Davis M., and Norman A. Portfolio selection with transaction costs. Mathematics of Operations Research 15 (1990) 676-713
14. Debreu G. Theory of value. Cowles Foundation Monograph vol. 17 (1959), Yale University Press, New Haven
15. Dermody J.C., and Prisman E.Z. No arbitrage and valuation in markets with realistic transactions costs. Journal of Financial and Quantitative Analysis 28 (1993) 65-80
16. Dybvig P.H., and Ross S.A. Arbitrage. In: Newman P., Milgate M., and Eatwell J. (Eds). The New Palgrave Dictionary of Money and Finance (1992), Palgrave Macmillan, London
17. Duffie D. Dynamic Asset Pricing Theory. third ed. (2001), Princeton University Press, Princeton
18. Edirisinghe C., Naik V., and Uppal R. Optimal replication of options with transaction costs and trading restrictions. Journal of Financial and Quantitative Analysis 28 (1993) 117-138
19. Garman M.B., and Ohlson J.A. Valuation of risky assets in arbitrage free economies with transaction costs. Journal of Financial Economics 9 (1981) 271-280
20. Gilster J., and Lee W. The effect of transaction costs and different borrowing and lending rates on the option pricing model. Journal of Finance 39 (1984) 1215-1221
21. Harrison J.M., and Kreps D.M. Martingales and arbitrage in multi-period securities markets. Journal of Economic Theory 20 (1979) 381-408
22. Hull J. Options, Futures and Other Derivatives. fifth ed. (2002), Prentice Hall
23. Ingersoll J.E. The subjective and objective evaluation of incentive stock options. Journal of Business 79 (2006) 453-487
24. Jouini E., and Kallal H. Martingales and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1995) 178-197
25. Jouini E., and Kallal H. Arbitrage in securities markets with short-sales constraints. Mathematical Finance 5 (1995) 197-232
26. Karatzas I. Lectures on the Mathematics of Finance (1996), American Mathematical Society, Providence
27. Karatzas I., and Kou S.G. On the pricing of contingent claims under constraints. The Annals of Applied Probability 6 (1996) 321-369
28. King A. Duality and Martingales: A stochastic programming perspective on contingent claims. Mathematical Programming, Series B 91 (2002) 543-562
29. King, A., Koivu, M., Pennanen, T., 2002. Calibrating Option Bounds, Working Paper, Helsinki School of Economics.
30. Luenberger D.G. Investment Science (1998), Oxford University Press, New York
31. Leland H. Option pricing and replication with transaction costs. Journal of Finance 40 (1985) 1283-1301
32. Magill M., and Constantinides G. Portfolio selection with transaction costs. Journal of Economic Theory 13 (1976) 264-271
33. Mangasarian O.L. Nonlinear Programming (1969), McGraw-Hill, New York
34. Merton R. Theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1973) 141-183
35. Merton R. Continuous Time Finance. second ed. (1992), Basil Blackwell, Oxford and Cambridge
36. Murtagh B., and Saunders M. Large-scale linearly constrained optimization. Mathematical Programming 14 (1978) 41-72
37. Naik V. Finite state securities market models and arbitrage. In: Jarrow R.A., Maksimovic V., and Ziemba W.T. (Eds). Finance, Handbooks in Operations research and management Science vol. 9 (1995), Elsevier 31-64
38. Napp C. Pricing issues with investment flows, applications to market models with frictions. Journal of Mathematical Economics 35 (2001) 383-408
39. Napp C. The Dalang-Morton-Willinger theorem under cone constraints. Journal of Mathematical Economics 39 (2003) 111-126
40. Pliska S.R. Introduction to Mathematical Finance: Discrete Time Models (1997), Blackwell Publishers, Oxford
41. Prisman E.Z. Valuation of risky assets in arbitrage free economies with frictions. Journal of Finance 41 (1986) 545-557
42. Rockafellar R.T. Conjugate Duality and Optimization (1974), Society for Industrial and Applied Mathematics, Philadelphia
43. Ross S.A. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13 (1976) 341-360
44. Ross S.A. Return, risk, and arbitrage. In: Friend I., and Bicksler J.L. (Eds). Risk and Return in Finance (1977), Ballinger Publishing company, Cambridge, MA
45. Ross S.A. A simple approach to the valuation of risky streams. Journal of Business 51 (1978) 453-475
46. Ross S.A. Arbitrage and martingales with taxation. Journal of Political Economy 95 (1987) 371-393
47. Stiemke E. Über positive Lösungen homogener linearer Gleichungen. Mathematische Annalen 76 (1915) 340-342
48. Tucker A. Dual systems of homogeneous linear relations. In: Kuhn H., and Tucker A. (Eds). Linear Inequalities and Related Systems. Annals of Mathematics Studies vol. 38 (1956), Princeton University Press, Princeton
49. Zhao, Y., Ziemba, W.T., 2003. On Leland's option pricing and hedging strategy with transaction costs. Working Paper, Nanyang Business School, Nanyang Technological University.
50. Zhao Y., and Ziemba W.T. On Leland's option pricing and hedging strategy with transactions costs. Finance Research Letters 4 (2007) 49-58