Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: finite energy functional spaces; unbounded domains with a cut Includes bibliographical references (leaf 29).

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

The importance of Orlicz spaces in the study of mathematics of nance came to the for in the 2000's when Frittelli and his collaborators connected the theory of utility functions to Orlicz spaces. In this thesis, we look at how Orlicz spaces play a role in nancial mathematics. After giving an overview of scalar-valued Orlicz spaces, we look at the rst fundamental theorem of asset pricing in an Orlicz space setting. We then give a brief summary of scalar risk measures, followed by the representation result for convex risk measures on Orlicz hearts. As an example of a risk measure, we take a detailed look at the Wang transform both as a pricing mechanism and as a risk measure. As the theory of nancial mathematics is moving towards the set-valued setting, we give a description of vector-valued Orlicz hearts and their duals using tensor products. Lastly, we look at set-valued risk measures on Orlicz hearts, proving a robust representation theorem via a tensor product approach.

Thesis (Ph. D.)--University of Hong Kong, 1987.

published_or_final_version / abstract / toc / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

We consider the problem of characterising Besov-Lipshitz and Triebel-Lizorkin spaces using kernels with limited smoothness and decay. This extends the work of H.-Q. Bui et al in [4] and [5] from kernels in S to more general kernels, including the Poisson kernel. We overcome the difficulty of defining the convolution of a general kernel with a distribution by using the concept of a bounded distribution introduced by E. Stein [12]. The characterisations we obtain are valid for the full range of indices.