creator Zhang, Zhao advisor Bielecki, Tomasz advisor Cialenco, Igor This thesis presents a unified framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures. In particular, we establish a duality between them. We derive representation theorems for both dynamic coherent acceptability indices and dynamic coherent risk measures in terms of so called dynamically consistent sequence of sets of probability measures. In addition, we present an alternative approach to study dynamic coherent acceptability indices and the representation theorem. Finally, we provide examples and counterexamples of dynamic coherent acceptability indices, and their applications in portfolio management. Submitted by Dana Lamparello (dlampare@iit.edu) on 2011-11-30T22:27:50Z No. of bitstreams: 2 Zhao Zhang_PhD Thesis.pdf: 2341761 bytes, checksum: 0dca394d224ef37889bbaa127a723370 (MD5) Title Page with Signature.pdf: 119121 bytes, checksum: 375dfeb39fa28c9eb28fd025b234042b (MD5) Made available in DSpace on 2011-11-30T22:27:50Z (GMT). No. of bitstreams: 2 Zhao Zhang_PhD Thesis.pdf: 2341761 bytes, checksum: 0dca394d224ef37889bbaa127a723370 (MD5) Title Page with Signature.pdf: 119121 bytes, checksum: 375dfeb39fa28c9eb28fd025b234042b (MD5) Previous issue date: 2011-05 Ph.D. in Applied Mathematics, May 2011 2011-05-02 2011-05 http://hdl.handle.net/10560/2352 en Dissertation born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department