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Arbitrage and Optimal Portfolio Choice with Financial Constraints

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Abstract

We analyze the pricing of risky income streams in a world with competitive security markets where investors are constrained by restrictions on possible portfolio holdings. We investigate how we can transfer concepts and pricing techniques from a world without frictions to such a more realistic situation. We show that basically two new aspects arise: First, portfolio constraints can lead to situations where not all arbitrage opportunities are necessarily eliminated in equilibrium. For a world with portfolio constraints the concept of no arbitrage has to be replaced by a weaker concept which we call no unlimited arbitrage. Second, though we can characterize prices which allow no unlimited arbitrage by the existence of certain state prices as in the unconstrained case, additional computational work is needed for deriving from this fact a pricing theory for contingent claims. We propose a technique which can achieve this task and which renders itself for a computationally simple implementation for many constraint situations which are of practical interest. The power of no arbitrage techniques is preserved in the sense that no specific assumptions about utility functions of investors have to be made. We relate our analysis to the optimal decision problem of an investor and show the various relations between the properties of an optimal solution to this problem and the arbitrage-free values of risky income streams. This opens a unified view on the different approaches to asset pricing under portfolio constraints used in the literature and conveys their common underlying logic.

Suggested Citation

  • Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
  • Handle: RePEc:onb:oenbwp:49
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    Cited by:

    1. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    2. Jürgen Eichberger & Klaus Rheinberger & Martin Summer, 2014. "Credit risk in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 407-435, October.
    3. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    4. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    5. V.F. Martins-da-Rocha & L. Triki, 2005. "Equilibria in exchange economies with financial constraints: Beyond the Cass Trick," Microeconomics 0503013, EconWPA.

    More about this item

    Keywords

    Arbitrage; Portfolio Constraints; Asset Pricing;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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