The study of metric spaces is closely related to the study of topology in that the study of metric spaces concerns itself, also, with sets of points and with a limit point concept based on a function which gives a "distance" between two points. In some topological spaces it is possible to define a distance function between points in such a way that a limit point of a set in the topological sense is also a limit point of the same set in a metric sense. In such a case the topological space is "metrizable". The real numbers with its usual topology is an example of a topological space which is metrizable, the distance function being the absolute value of the difference of two real numbers. Chapters II and III of this thesis attempt to classify, to a certain extent, what type of topological space is metrizable. Chapters IV and V deal with several properties of metric spaces and certain functions of metric spaces, respectively.

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.

Habilitationsschrift--Bonn. / Bibliography: p. 81.

Thesis (M. Arch.)--University of Hong Kong, 2000. / Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2001. / Includes bibliographical references.

Thesis (M.L.A.)--University of Hong Kong, 1999. / Includes special study report entitled: Factory-made street furniture : outdoor seating. Includes bibliographical references.

Thesis (M. Arch.)--University of Hong Kong, 2001. / Includes special study report entitled: Corner building : a structure with a roof and walls that locates at the places where two streets meet. Includes bibliographical references.

Thesis (M.U.D.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 137).

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Habilitationsschrift--Bonn. / Bibliography: p. 81.