, Volume 13, Issue 1, pp 201–224 | Cite as

Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets

  • Frank Oertel
  • Mark P. Owen


This paper is devoted to a further generalisation of the main results in [5] including the representation of the weak super-replication price (cf. equation (1.6)). In addition to the already established weakening of the technical assumptions in [5] (cf. [24] and [25]), the main results in [5] can be still generalised by considering the geometric structure of the underlying problem (based on the properties of Riesz spaces and polar wedges therein). In Section 5 we show under which geometric conditions of the relevant sets the results still hold (cf. Theorem 5.3 and Corollary 5.5). In particular, we can completely remove the restrictive admissibility assumption and carry forward equation (1.4) to a larger class of wedges \(K \subseteq L^{0}\) (cf. Corollary 5.5).


Super-replication Incomplete markets Contingent claims Duality theory Weak topologies Riesz spaces 

Mathematics Subject Classification (2000)

1B16 46N10 60G44 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Frank Oertel
    • 1
  • Mark P. Owen
    • 2
  1. 1.Department of MathematicsUniversity College CorkCorkIreland
  2. 2.Department of Actuarial Mathematics and StatisticsMaxwell Institute for Mathematical Sciences and Heriot-Watt UniversityEdinburghScotland

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