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Superhedging in illiquid markets

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  • Teemu Pennanen

Abstract

We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. We derive dual characterizations of superhedging conditions for contingent claim processes in a market without a cash account. The characterizations are given in terms of stochastic discount factors that correspond to martingale densities in a market with a cash account. The dual representations are valid under a topological condition and a weak consistency condition reminiscent of the ``law of one price'', both of which are implied by the no arbitrage condition in the case of classical perfectly liquid market models. We give alternative sufficient conditions that apply to market models with nonlinear cost functions and portfolio constraints.

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  • Teemu Pennanen, 2008. "Superhedging in illiquid markets," Papers 0807.2962, arXiv.org.
    • Handle: RePEc:arx:papers:0807.2962
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    References listed on IDEAS

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    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    2. Jean-Michel Courtault & Freddy Delbaen & Yuri Kabanov & Christophe Stricker, 2004. "On the law of one price," Finance and Stochastics, Springer, vol. 8(4), pages 525-530, November.
    3. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627, October.
    4. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
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    Cited by:

    1. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    2. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.

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