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Viability and Equilibrium in Securities Markets with Frictions

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  • Elyès Jouini
  • Hédi Kallal

Abstract

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims-an underlying frictionless linear pricing rule-that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches-a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule-the supremum of the underlying frictionless linear pricing rules-for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules. Copyright Blackwell Publishers Inc 1999.

Suggested Citation

  • Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292.
  • Handle: RePEc:bla:mathfi:v:9:y:1999:i:3:p:275-292
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    Cited by:

    1. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    2. Jouini, Elyes & Kallal, Hedi, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 343-369.
    3. repec:gam:jrisks:v:5:y:2017:i:3:p:36-:d:105112 is not listed on IDEAS
    4. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    5. Jouini, Elyes & Kallal, Hedi & Napp, Clotilde, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 197-221, April.
    6. repec:dau:papers:123456789/5593 is not listed on IDEAS
    7. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
    8. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    9. repec:dau:papers:123456789/5590 is not listed on IDEAS
    10. Marcello Basili & Carlo Zappia, 2018. "Ellsberg’s Decision Rules and Keynes’s Long-Term Expectations," Department of Economics University of Siena 777, Department of Economics, University of Siena.
    11. Guangsug Hahn & Dong Chul Won, 2007. "Equilibrium in Financial Markets with Market Frictions," Korean Economic Review, Korean Economic Association, vol. 23, pages 267-302.
    12. Elyès Jouini & Clotilde Napp, 2002. "Arbitrage pricing and equilibrium pricing : compatibility conditions," Post-Print halshs-00176423, HAL.
    13. Cass, David & Siconolfi, Paolo & Villanacci, Antonio, 2001. "Generic regularity of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 61-76, September.
    14. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
    15. Baccara, Mariagiovanna & Battauz, Anna & Ortu, Fulvio, 2006. "Effective securities in arbitrage-free markets with bid-ask spreads at liquidation: a linear programming characterization," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 55-79, January.

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