creator Chen, Tao advisor Bielecki, Tomasz This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics. The contribution to mathematical finance is made via developing new theoretical results in the area of conic finance. Specifically, we have advanced dynamic aspects of conic finance by developing an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities using the theory of dynamic acceptability indices. This has been done within the framework of general probability spaces and discrete time. In the process, we have advanced the theory of dynamic sub-scale invariant performance measures. In particular, we proved a representation theorem of such measures in terms of a family of dynamic convex risk measures, and provided a representation of dynamic risk measures in terms of BS Es. The contribution to statistics is of fundamental importance as it initiates the theory underlying recursive computation of confidence regions for finite dimensional parameters in the context of stochastic dynamical systems. In the field of engineering, particularly in the field of control engineering, the area of recursive point estimation came to great prominence in the last forty years. However, there has been no work done with regard to recursive computation of confidence regions. To partially fill this gap, the second part of the thesis is devoted to recursive construction of confidence regions for parameters characterizing the one-step transition kernel of a time-homogeneous Markov chain. Submitted by Erma Thomas (thomase@iit.edu) on 2017-05-22T18:39:09Z No. of bitstreams: 1 etdadmin_upload_450541.zip: 798010 bytes, checksum: a62b4daf4f4a11a9faeb40b0e273e61a (MD5) Made available in DSpace on 2017-05-22T18:39:09Z (GMT). No. of bitstreams: 1 etdadmin_upload_450541.zip: 798010 bytes, checksum: a62b4daf4f4a11a9faeb40b0e273e61a (MD5) Previous issue date: 2016-07 Ph.D. In Applied Mathematics, July 2016 2016 2016-07 http://hdl.handle.net/10560/4082 en dynamic acceptability index dynamic conic finance g-expectation quasi-asymptotically linear estimator recursive confidence regions statistical inference for Markov chains 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