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Coherent acceptability measures in multiperiod models

By Berend Roorda, Hans Schumacher and Jacob Engwerda

Abstract

The framework of coherent risk measures has been introduced by Artzner et al. (1999) in a single-period setting. Here we investigate a similar framework in a multiperiod context. We add an axiom of dynamic consistency to the standard coherence axioms, and obtain a representation theorem in terms of collections of multiperiod probability measures that satisfy a certain product property. This theorem is similar to results obtained by Epstein and Schneider (2003) and Wang (2003) in a different axiomatic framework. We then apply our representation result to the pricing of derivatives in incomplete markets, extending results by Carr et al. (2001) to the multiperiod case. We present recursive formulas for the computation of price bounds and corresponding optimal hedges. When no shortselling constraints are present, we obtain a recursive formula for price bounds in terms of martingale measures

Topics: coherent risk measures, acceptability measures, dynamic consistency, robustness, option pricing, incomplete markets. JEL Classification, G11, G13
Year: 2004
OAI identifier: oai:CiteSeerX.psu:10.1.1.321.7457
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