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Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability

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  • Michail Anthropelos
  • Gordan Zitkovic

Abstract

In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled 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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  • Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
    • Handle: RePEc:arx:papers:0901.3318
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    File URL: http://arxiv.org/pdf/0901.3318
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    References listed on IDEAS

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    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612.
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    9. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
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    13. Damir Filipović & Michael Kupper, 2008. "Optimal Capital And Risk Transfers For Group Diversification," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 55-76.
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