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

Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets
Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets
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).
1385-1292
201-224
Oertel, Frank
5026be9a-a787-477f-bf94-23c72bd08ef5
Owen, Mark P.
3b927982-cf7d-44f5-8c3b-b7d6b03c5bdf
Oertel, Frank
5026be9a-a787-477f-bf94-23c72bd08ef5
Owen, Mark P.
3b927982-cf7d-44f5-8c3b-b7d6b03c5bdf

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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Published date: February 2009
Organisations: Mathematical Sciences

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Local EPrints ID: 347163
URI: http://eprints.soton.ac.uk/id/eprint/347163
ISSN: 1385-1292
PURE UUID: 225ad477-a8d2-4f85-bb10-42ff1120ccee

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Date deposited: 17 Jan 2013 16:22
Last modified: 14 Mar 2024 12:45

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Author: Frank Oertel
Author: Mark P. Owen

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