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Incomplete markets: transverse financial structures

Author

Listed:
  • Jean-Marc Bottazzi

    (CERMSEM, University Paris I Pantheon - Sorbonne, Maison des Sciences Economiques, 106-112 bd de l'Hôpital, 75647 Paris Cedex 13, FRANCE)

Abstract

In a multiperiod economy with incomplete markets and assets with payoff depending on the price history (e.g., asset and derivatives), we show that in order to get endowment generic existence of an equilibrium it is not needed to alter settlement features such as when payments are made and when the asset is traded. This is non-trivial as each such characteristic introduces a non-generic subclass of financial instruments. We show essentially that expiry date payments are the only payments that one needs perturbing (if at all). For previous periods - the P&L discovery map - is the one relevant for wealth transfers. This map transfers wealth between one period and the next by associating to each portfolio next period potential profit and losses as a function of the revealed information at the node. All present values involved can in general - because of backward induction pricing structure - be appropriately controlled via expiry payoffs only. This enables us to extend two-period work and introduce Transverse Financial Structures for multiperiod economies, where one cannot identify the payoffs of financial instruments to the P&L discovery map (in other words we introduce some financial ingeneering for Transverse Financial Structures). We capitalize on that difference using unexploited "maturity payout degrees of freedom" and rolling back the uncertainty tree. As an application of this approach we prove a conjecture by Magill and Quinzii that commodity forward contracts lead to endowment generic existence of an equilibrium in a multiperiod set-up.

Suggested Citation

  • Jean-Marc Bottazzi, 2002. "Incomplete markets: transverse financial structures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 67-82.
  • Handle: RePEc:spr:joecth:v:20:y:2002:i:1:p:67-82
    Note: Received: June 25, 1999; revised version: April 4, 2001
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    Cited by:

    1. Bottazzi, Jean-Marc & Luque, Jaime & Páscoa, Mário R., 2012. "Securities market theory: Possession, repo and rehypothecation," Journal of Economic Theory, Elsevier, vol. 147(2), pages 477-500.
    2. Busch, Lutz-Alexander & Govindan, Srihari, 2004. "Robust nonexistence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 641-645, September.

    More about this item

    Keywords

    Assets; Incomplete markets; Existence; Liquidity.;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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