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

Oertel, Frank and Owen, Mark P. (2009) Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets. Positivity, 13 (1), 201-224. (doi:10.1007/s11117-008-2196-9).

Record type: Article

Abstract

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).

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