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Teor. Veroyatnost. i Primenen., 1994, Volume 39, Issue 1, Pages 222–229 (Mi tvp3770)  

This article is cited in 29 scientific papers (total in 29 papers)

Short Communications

Large financial markets: asymptotic arbitrage and contiguity

Yu. M. Kabanova, D. O. Kramkovb

a Central Economics and Mathematics Institute, RAS
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce a large financial market as a sequence of ordinary security market models (in continuous or discrete time). An important property of such markets is the absence of asymptotic arbitrage, i.e., a possibility to obtain “essential” nonrisk profits from “infinitesimally” small endowments. It is shown that this property is closely related to the contiguity of the equivalent martingale measures. To check the “no asymptotic arbitrage” property one can use the criteria of contiguity based on the Hellinger processes. We give an example of a large market with correlated asset prices where the absence of asymptotic arbitrage forces the returns from the assets to approach the security market line of the CAPM.

Keywords: large security market, no-arbitrage, equivalent martingale measure, contiguity of measures, Hellinger process, Capital Asset Pricing Model (CAPM).

Full text: PDF file (513 kB)

English version:
Theory of Probability and its Applications, 1994, 39:1, 182–187

Bibliographic databases:

Received: 05.07.1993

Citation: Yu. M. Kabanov, D. O. Kramkov, “Large financial markets: asymptotic arbitrage and contiguity”, Teor. Veroyatnost. i Primenen., 39:1 (1994), 222–229; Theory Probab. Appl., 39:1 (1994), 182–187

Citation in format AMSBIB
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\by Yu.~M.~Kabanov, D.~O.~Kramkov
\paper Large financial markets: asymptotic arbitrage and contiguity
\jour Teor. Veroyatnost. i Primenen.
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\pages 222--229
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\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 1
\pages 182--187
\crossref{https://doi.org/10.1137/1139009}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. V. Gapeev, “Towards a proof of the first fundamental theorem of financial mathematics”, Russian Math. Surveys, 53:6 (1998), 1352–1353  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Hubalek F., Schachermayer W., “When does convergence of asset price processes imply convergence of option prices?”, Mathematical Finance, 8:4 (1998), 385–403  crossref  mathscinet  zmath  isi
    3. Klein I., “A fundamental theorem of asset pricing for large financial, markets”, Mathematical Finance, 10:4 (2000), 443–458  crossref  mathscinet  zmath  isi
    4. Klein I., “Free lunch for large financial markets with continuous price processes”, Annals of Applied Probability, 13:4 (2003), 1494–1503  crossref  mathscinet  zmath  isi
    5. De Donno M., Guasoni P., Pratellic M.P., Pratelli M., “Super–replication and utility maximization in large financial markets”, Stochastic Processes and Their Applications, 115:12 (2005), 2006–2022  crossref  mathscinet  zmath  isi
    6. Jouini E., Napp C., Schachermayer W., “Arbitrage and state price deflators in a general intertemporal framework”, Journal of Mathematical Economics, 41:6 (2005), 722–734  crossref  mathscinet  zmath  isi
    7. Klein I., “Market free lunch and large financial markets”, Annals of Applied Probability, 16:4 (2006), 2055–2077  crossref  mathscinet  zmath  isi
    8. Dempster M.A.H., Evstigneev I.V., Schenk-Hoppe K.R., “Volatility–induced financial growth”, Quantitative Finance, 7:2 (2007), 151–160  crossref  mathscinet  zmath  isi
    9. Klein I., “No asymptotic free lunch reviewed in the light of Orlicz spaces”, Seminaire de Probabilites XLI, Lecture Notes in Mathematics, 1934, 2008, 443–454  mathscinet  zmath  isi
    10. Campi L., “Mean–Variance Hedging in Large Financial Markets”, Stochastic Analysis and Applications, 27:6 (2009), 1129–1147  crossref  mathscinet  zmath  isi
    11. D. B. Rokhlin, “On the Existence of an Equivalent Supermartingale Density for a Fork-Convex Family of Stochastic Processes”, Math. Notes, 87:4 (2010), 556–563  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Di Nunno G., Eide I.B., “Minimal-Variance Hedging in Large Financial Markets: Random Fields Approach”, Stoch Anal Appl, 28:1 (2010), 54–85  crossref  mathscinet  zmath  isi
    13. Kardaras C., “Market Viability via Absence of Arbitrage of the First Kind”, Financ. Stoch., 16:4 (2012), 651–667  crossref  isi
    14. Klein I. Lepinette E. Perez-Ostafe L., “Asymptotic Arbitrage With Small Transaction Costs”, Financ. Stoch., 18:4 (2014), 917–939  crossref  isi
    15. Strong W., “Fundamental Theorems of Asset Pricing For Piecewise Semimartingales of Stochastic Dimension”, Financ. Stoch., 18:3 (2014), 487–514  crossref  isi
    16. Cordero F., Perez-Ostafe L., “Critical Transaction Costs and 1-Step Asymptotic Arbitrage in Fractional Binary Markets”, Int. J. Theor. Appl. Financ., 18:5 (2015), 1550029  crossref  isi
    17. Fontana C., “Weak and Strong No-Arbitrage Conditions For Continuous Financial Markets”, Int. J. Theor. Appl. Financ., 18:1 (2015), 1550005  crossref  isi
    18. Chau H.N. Tankov P., “Market Models With Optimal Arbitrage”, SIAM J. Financ. Math., 6:1 (2015), 66–85  crossref  isi
    19. M. Rásonyi, J. G. Rodriguea-Villareal, “Optimal investment under behavioral criteria in incomplete diffusion market models”, Theory Probab. Appl., 60:4 (2016), 631–646  mathnet  crossref  crossref  mathscinet  isi  elib
    20. Rasonyi M., “on Optimal Strategies For Utility Maximizers in the Arbitrage Pricing Model”, Int. J. Theor. Appl. Financ., 19:7 (2016), 1650047  crossref  mathscinet  zmath  isi  elib  scopus
    21. Kabanov Yu., Kardaras C., Song Sh., “No arbitrage of the first kind and local martingale num?raires”, Financ. Stoch., 20:4 (2016), 1097–1108  crossref  mathscinet  zmath  isi  elib  scopus
    22. Cordero F., Perez-Ostafe L., “Strong asymptotic arbitrage in the large fractional binary market”, Math. Financ. Econ., 10:2 (2016), 179–202  crossref  mathscinet  zmath  isi  scopus
    23. Klein I. Schmidt T. Teichmann J., “No Arbitrage Theory For Bond Markets”, Advanced Modelling in Mathematical Finance: in Honour of Ernst Eberlein, Springer Proceedings in Mathematics & Statistics, ed. Kallsen J. Papapantoleon A., Springer International Publishing Ag, 2016, 381–421  crossref  isi
    24. Rasonyi M., “Maximizing Expected Utility in the Arbitrage Pricing Model”, J. Math. Anal. Appl., 454:1 (2017), 127–143  crossref  isi
    25. Mostovyi O., “Utility Maximization in a Large Market”, Math. Financ., 28:1 (2018), 106–118  crossref  isi
    26. Robertson S., Spiliopoulos K., “Indifference Pricing For Contingent Claims: Large Deviations Effects”, Math. Financ., 28:1 (2018), 335–371  crossref  isi
    27. Roch A., “Asymptotic Asset Pricing and Bubbles”, Math. Financ. Econ., 12:2 (2018), 275–304  crossref  isi
    28. Rasonyi M., “On Utility Maximization Without Passing By the Dual Problem”, Stochastics, 90:7 (2018), 955–971  crossref  mathscinet  isi  scopus
    29. Palmowski Z. Stettner L. Sulima A., “Optimal Portfolio Selection in An Ito-Markov Additive Market”, Risks, 7:1 (2019), 34  crossref  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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