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Incomplete markets, transaction costs and liquidity effects

  • E. Jouini
  • P. -F. Koehl
  • N. Touzi

An agent's optimization problem of the expected terminal wealth utility in a trinomial tree economy is solved. At each transaction date, the agent can trade in a riskless asset, a primitive asset subject to constant proportional transaction costs, and a contingent claim characterized by some parameter kappa whose bid and ask price is defined by allowing for different equivalent martingale measures. In addition to the classical portfolio choice problem, the characteristic of the contingent claim κ is determined endogenously in the optimization problem. Under suitable conditions, it is proved that the optimal demand of the agent in the primitive risky asset is zero independently of the choice of the terminal wealth utility function: the agent prefers not to trade in the asset subject to transaction costs, which prevents the market from being complete, rather than trading in both assets. Next, the optimal choice of the contingent claim is characterized and the results are applied to European call and put options with fixed maturity and varying exercise price κ.

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Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

Volume (Year): 3 (1997)
Issue (Month): 4 ()
Pages: 325-347

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Handle: RePEc:taf:eurjfi:v:3:y:1997:i:4:p:325-347
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  1. Duffie Darrell & Rahi Rohit, 1995. "Financial Market Innovation and Security Design: An Introduction," Journal of Economic Theory, Elsevier, vol. 65(1), pages 1-42, February.
  2. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
  3. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  4. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
  5. Bajeux, I. & Rochet, J.C., 1994. "Dynamic Spanning: Are Options an Appropriate Instrument?," Papers 94.329, Toulouse - GREMAQ.
  6. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  7. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November.
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