COHERENT ACCEPTABILITY MEASURES IN MULTIPERIOD MODELS

Berend Roorda, Johannes Schumacher and Jacob Engwerda

Mathematical Finance, 2005, vol. 15, issue 4, 589-612

Abstract: The framework of coherent risk measures has been introduced by Artzner et al. (1999; Math. Finance 9, 203–228) 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; J. Econ. Theor. 113, 1–31) and Wang (2003; J. Econ. Theor. 108, 286–321) in a different axiomatic framework. We then apply our representation result to the pricing of derivatives in incomplete markets, extending results by Carr, Geman, and Madan (2001; J. Financial Econ. 32, 131–167) 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.

Date: 2005
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