No free lunch and risk measures on Orlicz spaces
Date
2012-09-12
Authors
Offwood, Theresa Maria
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Abstract
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.