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Coherent risk measures in general economic models and price bubbles

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  • Kountzakis, C.
  • Polyrakis, I.A.

Abstract

In this article we study coherent risk measures in general economic models where the set of financial positions is an ordered Banach space E and the safe asset an order unit x0 of E. First we study some properties of risk measures. We show that the set of normalized (with respect to x0) price systems is weak star compact and by using this result we prove a maximum attainment representation theorem which improves the one of Jaschke and Küchler (2001). Also we study how a risk measure changes under different safe assets and we show a kind of equivalence between these risk measures. In the sequel we study subspaces of E consisting of financial positions of risk greater or equal to zero and we call these subspaces unsure. We find some criteria and we give examples of these subspaces. In the last section, we combine the unsure subspaces with the theory of price-bubbles of Gilles and LeRoy (1992).

Suggested Citation

  • Kountzakis, C. & Polyrakis, I.A., 2013. "Coherent risk measures in general economic models and price bubbles," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 201-209.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:3:p:201-209
    DOI: 10.1016/j.jmateco.2013.02.002
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    References listed on IDEAS

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    1. Christian Gilles & Stephen F. LeRoy, 1997. "Bubbles as payoffs at infinity (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 261-281.
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    Cited by:

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    2. Panagiotis Xidonas & Christos E. Kountzakis & Christis Hassapis & Christos Staikouras, 2016. "RAROC in portfolio optimization," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-14, September.
    3. Bernardi Mauro & Roy Cerqueti & Arsen Palestini, 2016. "Allocation of risk capital in a cost cooperative game induced by a modified Expected Shortfall," Papers 1608.02365, arXiv.org.

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