Summary
We consider a general framework covering models of financial markets with transaction costs. Assuming that the solvency cones are proper and evolve in time continuously we prove a hedging theorem describing the set of initial endowments allowing to hedge a vector-valued contingent claim by a self-financing portfolio.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bouchard B., Kabanov Yu.M., Touzi N. Option pricing by large risk aversion utility under transaction costs. Decisions in Economics and Finance, 24 (2001), 2, 127 - 136.
Cvitanie J., Karatzas I. Hedging and portfolio optimization under transaction costs: a martingale approach. Mathematical Finance, 6 (1996), 2, 133 - 165.
Cvitanié J., Pham H., Touzi N. A closed form solution to the problem of super-replication under transaction costs. Finance and Stochastics, 3 (1999), 35 - 54.
Delbaen, F. Martingale measures when asset prices are continuous and bounded. Mathematical Finance, 2 (1992), 107 - 130.
Delbaen F., Kabanov Yu.M, Valkeila S. Hedging under transaction costs in currency markets: a discrete-time model. Mathematical Finance, 12 (2002), 1, 45 - 61.
Delbaen F., Schachermayer W. A general version of the fundamental theorem of asset pricing. Math. Annalen, 300 (1994), 463 - 520.
Dunford N., Schwartz J.T. Linear Operators. Part I: General Theory. Wiley, NY, 1988.
Föllmer H., Kabanov Yu.M. Optional decomposition and Lagrange multipliers. Finance and Stochastics, 2 (1998), 1, 69 - 81.
Föllmer H., Kramkov D.O. Optional decompositions under constraints. Probability Theory and Related Fields, 109 (1998), 1, 1 - 25.
Jouini, E., Kallal H. Martingales and arbitrage in securities markets with transaction costs. J. Economic Theory, 66 (1995), 178 - 197.
Kabanov Yu.M. Hedging and liquidation under transaction costs in currency markets. Finance and Stochastics, 3 (1998), 237 - 248.
Kabanov Yu.M. The arbitrage theory. In: Handbooks in Mathematical Finance: Topics in Option Pricing, Interest Rates and Risk Management. Cambridge University Press, 2001.
Kabanov, Yu.M., Last, G. Hedging in a model with transaction costs. To appear in Proceedings of Steklov Mathematical Institute.
Kabanov Yu.M., Last G. Hedging under transaction costs in currency markets: a continuous-time model. Mathematical Finance, 12 (2002), 1, 63 - 70.
Kabanov Yu.M., Râsonyi M., Stricker Ch. No-arbitrage criteria for financial markets with efficient friction. Finance and Stochastics, 6 (2002), 3.
Kabanov Yu.M., Râsonyi M., Stricker Ch. On the closedness of sums of convex cones in L° and the robust no-arbitrage property. Preprint, December, 2001.
Kramkov D.O. Optional decomposition of supermartingales and hedging in incomplete security markets. Probability Theory and Related Fields, 105 (1996), 4, 459 - 479.
Levental S., Skorohod A.V. On the possibility of hedging options in the presence of transaction costs. The Annals of Applied Probability, 7 (1997), 410 - 443.
Megginson R.E. An Introduction to Banach Space Theory. Springer, BerlinHeidelberg—New York, 1998.
Penner I. Arbitragefreiheit in Finanzmärkten mit Transaktionkosten. Diplomarbeit, Humboldt—Universität zu Berlin, June, 2001.
Sin C.A. Strictly local martingales and hedge ratios on stochastic volatility models. PhD—dissertation, Cornell University, 1996.
Schachermayer W. The Fundamental Theorem of Asset Pricing under proportional transaction costs in finite discrete time. Preprint, November, 2001.
Stricker Ch., Yan J.A. Some remarks on the optional decomposition theorem. Séminaire de Probabilités XXXII. Lect. Notes Math., 1686 (1998), 56 - 66.
Soner H.M., Shreve S.E., Cvitanic J. There is no nontrivial hedging portfolio for option pricing with transaction costs. The Annals of Applied Probability, 5 (1995), 327 - 355.
Touzi N. Super-replication under proportional transaction costs: from discrete to continuous-time models. Math. Meth. Oper. Res., 50 (1999), 297 - 320.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kabanov, Y.M., Stricker, C. (2002). Hedging of Contingent Claims under Transaction Costs. In: Sandmann, K., Schönbucher, P.J. (eds) Advances in Finance and Stochastics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04790-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-04790-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07792-0
Online ISBN: 978-3-662-04790-3
eBook Packages: Springer Book Archive