Dynamic Coherent Acceptability Indices and Their Applications to Finance

31 Pages Posted: 11 Jun 2014

See all articles by Tomasz R. Bielecki

Tomasz R. Bielecki

Illinois Institute of Technology

Igor Cialenco

Illinois Institute of Technology

Zhao Zhang

Illinois Institute of Technology

Date Written: July 2014

Abstract

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‚Äźcalled 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.

Keywords: dynamic coherent acceptability index, dynamic measures of performance, dynamic coherent risk measures, dynamically consistent sequence of sets of probability measures, time consistency, dynamic GLR, dynamic RAROC

Suggested Citation

Bielecki, Tomasz R. and Cialenco, Igor and Zhang, Zhao, Dynamic Coherent Acceptability Indices and Their Applications to Finance (July 2014). Mathematical Finance, Vol. 24, Issue 3, pp. 411-441, 2014, Available at SSRN: https://ssrn.com/abstract=2448770 or http://dx.doi.org/10.1111/j.1467-9965.2012.00524.x

Tomasz R. Bielecki (Contact Author)

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 W. 32nd Street
Chicago, IL 60616
United States
312 567 3185 (Phone)
312 567 3135 (Fax)

Igor Cialenco

Illinois Institute of Technology ( email )

Department of Applied Mathematics
10 West 32nd Str, Bld E1, Room 208
Chicago, IL 60616
United States
3125673131 (Phone)

HOME PAGE: http://math.iit.edu/~igor/

Zhao Zhang

Illinois Institute of Technology ( email )

Stuart Graduate School of Business
565 W. Adams St.
Chicago, IL 60661
United States

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