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DYNAMIC COHERENT ACCEPTABILITY INDICES AND THEIR APPLICATIONS TO FINANCE
Author(s) -
Bielecki Tomasz R.,
Cialenco Igor,
Zhang Zhao
Publication year - 2014
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2012.00524.x
Subject(s) - duality (order theory) , portfolio , representation (politics) , sequence (biology) , representation theorem , mathematical economics , econometrics , computer science , economics , mathematics , finance , pure mathematics , politics , biology , political science , law , genetics
In this paper, we present a theoretical framework for studying coherent acceptability indices (CAIs) in a dynamic setup. We study dynamic CAIs (DCAIs) and dynamic coherent risk measures (DCRMs), and we establish a duality between them. We derive a representation theorem for DCRMs in terms of a so‐called dynamically consistent sequence of sets of probability measures. Based on these results, we give a specific construction of DCAIs. We also provide examples of DCAIs, both abstract and also some that generalize selected classical financial measures of portfolio performance.