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Partial equilibria with convex capital requirements: existence, uniqueness and stability

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Abstract

We consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims in an incomplete semimartingale model of a financial market. Assuming that the agents’ risk preferences are modeled by convex capital requirements, we define and analyze their demand functions and propose a notion of a partial equilibrium price. In addition to sufficient conditions for the existence and uniqueness, we also show that the equilibrium prices are stable with respect to misspecifications of agents’ risk preferences.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712, USA

    Michail Anthropelos & Gordan Žitković

Authors
  1. Michail Anthropelos
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  2. Gordan Žitković
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Correspondence to Gordan Žitković.

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Both authors were supported in part by the National Science Foundation under award number DMS-0706947 during the preparation of this work. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation.

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Anthropelos, M., Žitković, G. Partial equilibria with convex capital requirements: existence, uniqueness and stability. Ann Finance 6, 107–135 (2010). https://doi.org/10.1007/s10436-009-0134-x

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