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Pareto Equilibria with coherent measures of risk

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  • David Heath
  • Hyejin Ku

Abstract

In this paper, we provide a definition of Pareto equilibrium in terms of risk measures, and present necessary and sufficient conditions for equilibrium in a market with finitely many traders (whom we call “banks”) who trade with each other in a financial market. Each bank has a preference relation on random payoffs which is monotonic, complete, transitive, convex, and continuous; we show that this, together with the current position of the bank, leads to a family of valuation measures for the bank. We show that a market is in Pareto equilibrium if and only if there exists a (possibly signed) measure that, for each bank, agrees with a positive convex combination of all valuation measures used by that bank on securities traded by that bank.

Suggested Citation

  • David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172, April.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:2:p:163-172
    DOI: 10.1111/j.0960-1627.2004.00187.x
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