Consistent Risk Measures and a non-linear Extension of Backwards Martingale Convergence.

[en] We study the behavior of conditional risk measures along decreasing σ-fields. Under a condition of consistency, we prove a non-linear extension of backwards martingale convergence. In particular we show the existence of a limiting conditional risk measure with respect to the tail field, we describe its dual representation in terms of a limiting penalty function, and we show that consistency extends to the tail field. Moreover, we clarify the structure of global risk measures which are consistent with the given sequence of conditional risk measures.

Disciplines :

Mathematics

Author, co-author :

Föllmer, Hans ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit

Penner, Irina

External co-authors :

yes

Language :

English

Title :

Consistent Risk Measures and a non-linear Extension of Backwards Martingale Convergence.

Publication date :

2015

Main work title :

Festschrift Masatoshi Fukushima

Editor :

Z.-Q. Chen

N. Jacob

M. Takeda

Publisher :

World Scientific

ISBN/EAN :

978-981-4596-52-7

Collection name :

Interdisciplinary Mathematical Sciences, Vol. 17

Pages :

183-202

Available on ORBilu :

since 25 March 2016

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Bibliography

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