Skip to main content
SpringerLink
Log in

On Computation of Arbitrage for Markets with Friction

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

Included in the following conference series:

Abstract

We are interested in computation of locating arbitrage in financial markets with frictions. We consider a model with a finite number of financial assets and a finite number of possible states of nature. We derive a negative result on computational complexity of arbitrage in the case when securities are traded in integer numbers of shares and with a maximum amount of shares that can be bought for a fixed price (as in reality). When these conditions are relaxed, we show that polynomial time algorithms can be obtained by applying linear programming techniques. We also establish the equivalence for no-arbitrage condition & optimal consumption portfolio.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allingham, M., 1991. Arbitrage, St. Martin’s Press, New York.

    Google Scholar 

  2. Ardalan, K., The no-arbitrage condition and financial markets with transaction costs and heterogeneous information: the bid-ask spread, Global Finance Journal, 1999, 10(1): 83.

    Article  MathSciNet  Google Scholar 

  3. Arrow, K. J., Debreu, G., Existence of an equilibrium for a competitive economy, Econometrica, 1954, 22: 265.

    Article  MATH  MathSciNet  Google Scholar 

  4. Black, F., Sholes, M., The pricing of options and corporate liabilities, Journal of Political Economy, 1973, 81: 637.

    Article  Google Scholar 

  5. Borwein, J.M., 1977. Proper Efficient Points for Maximizations with Respect to Cones. SIAM Journal on Control and Optimization 15, 1977, pp. 57–63.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. C. Cox and C. F. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory 49 (1989), 33–83.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dermody, J. C., Prisman, E.Z., No arbitrage and valuation in market with realistic transaction costs, Journal of Financial and Quantitative Analysis 1993, 28(1): 65.

    Article  Google Scholar 

  8. J. B. Detemple and F. Zapatero, Optimal consumption-portfolio policies with habit formation, Mathematical Finance2 (1992), no. 4, 251–274.

    Article  MATH  Google Scholar 

  9. Duffie, D., Dynamic asset pricing theory, 2nd ed., Princeton University Press, New Jersey, 1996.

    Google Scholar 

  10. P. Dybvig and S. Ross, Arbitrage, in The New Palgrave: A Dictionary of Economics, 1, J. Eatwell, M. Milgate and P. Newman, eds., London: McMillan, 1987,, pp. 100–106.

    Google Scholar 

  11. Garey, M. R., Johnson, D.S., Computers and Intractability: a Guide to the Theory of NP-completeness, New York: W.H. Freeman, 1979.

    MATH  Google Scholar 

  12. Garman, M. B., Ohlson, J.A., Valuation of risky assets in arbitrage-free economies with transactions costs, Journal of Financial Economics, 1981, 9: 271.

    Article  Google Scholar 

  13. R. C. Green, and S. Srivastava, “Risk Aversion and Arbitrage”, The Journal of Finance, Vol. 40, pp. 257–268, 1985.

    Article  MathSciNet  Google Scholar 

  14. N. H. Hakansson, Optimal investment and consumption strategies under risk for a class of utility functions, Econometrica38 (1970), no. 5, 587–607.

    Article  MATH  Google Scholar 

  15. H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constrains: the infinite dimensional case, Journal of Economic Theory 54 (1991), 259–304.

    Article  MATH  MathSciNet  Google Scholar 

  16. H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constrains: the finite dimensional case, Mathematical Finance 1(1991), no. 3, 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  17. Hirsch, M. D., Papadimitriou, C. H., Vavasis, S. A., Exponential lower bounds for finding brouwer fixed points, Journal of Complexity, 1979, 5: 379.

    Article  MathSciNet  Google Scholar 

  18. I. Karatzas, J. P. Lehoczky, and S. E. Shreve, Optimal portfolio and consumption decisions for a “small investor” on a finite horizon, SIAM Journal on Control and Optimization25 (1987), no. 6, 1557–1586.

    Article  MATH  MathSciNet  Google Scholar 

  19. Merton, R.C., 1973. Theory of Rational Option Pricing. Bell Journal of Economics and Management Science 4, 141–183.

    Article  MathSciNet  Google Scholar 

  20. R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory 3 (1971), 373–413.

    Article  MathSciNet  Google Scholar 

  21. H. Pham and N. Touzi, The fundamental theorem of asset pricing with cone constraints, Journal of Mathematical Economics, 31, 265–279, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  22. R. T. Rockafellar, Convex AnalysisPrinceton, New Jersey, Princeton University Press, 1970.

    MATH  Google Scholar 

  23. Ross, S.A., The arbitrage theory of capital asset pricing, Journal of Economic Theory, 1976, 13: 341.

    Article  MathSciNet  Google Scholar 

  24. S. A. Ross, “Return, Risk and Arbitrage”, Risk and Return in Finance, Friend and Bicksler (eds.), Cambridge, Mass., Ballinger, pp. 189–218, 1977.

    Google Scholar 

  25. Scarf, H., The Computation of Economic Equilibria, New Haven: Yale University Press, 1973.

    Google Scholar 

  26. S. P. Sethi, Optimal consumption and investment with bankruptcy, Kluwer, Boston, 1997.

    Google Scholar 

  27. H. Shirakawa, Optimal consumption and portfolio selection with incomplete markets and upper and lower bound constaints, Mathematical Finance 4 (1994), no. 1, 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  28. H. Shirakawa and H. Kassai, Optimal consumption and arbitrage in incomplete, finite state security markets, Journal of Operations Research 45 (1993), 349–372.

    Article  MATH  MathSciNet  Google Scholar 

  29. S. E. Shreve, H. M. Soner, and G.-L. Xu, Optimal investment and consumption with two bounds and transaction costs, tMathematical Finance 1 (1991), no. 3, 53–84.

    Article  MATH  Google Scholar 

  30. Smith, A., An Inquiry into the Nature and Causes of the Wealth of Nations, Modern Library, 1937.

    Google Scholar 

  31. Spremann, K., The simple analytics of arbitrage, Capital Market Equilibria(ed.Bamberg, G., Spremann, K.), New York: Springer-Verlag, 1986, pp. 189–207.

    Google Scholar 

  32. Wilhelm, J., Arbitrage Theory, Berlin: Springer-Verlag, 1985.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Hong Kong, P. R. China

    Xiaotie Deng

  2. Institute of Systems Science, Chinese Academy of Sciences, Beijing, P.R. China

    Zhongfei Li

  3. Academy of Mathematical and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China

    Shouyang Wang

Authors
  1. Xiaotie Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongfei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shouyang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Deng, X., Li, Z., Wang, S. (2000). On Computation of Arbitrage for Markets with Friction. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_31

Download citation

  • DOI: https://doi.org/10.1007/3-540-44968-X_31

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation