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| Type | Bachelor's Thesis |
| Scope | Discipline-based scholarship |
| Title | Risk measures: the interplay of eligible assets and acceptance sets |
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| Institution | University of Zurich |
| Faculty | Faculty of Business, Economics and Informatics |
| Number of Pages | 40 |
| Date | 2020 |
| Abstract Text | We provide an overview of relevant concepts in the context of eligible assets, risk measures and acceptance sets. Since the publication of the landmark paper by Artzner, Delbaen, Eber and Heath in 1999, the bulk of the literature has focused on risk measures corresponding to a risk-free eligible asset, namely cash-additive risk measures. Recently, the focus has shifted towards risk measures corresponding to general eligible assets that need not necessarily be essentially bounded away from zero. We prove the standard correspondence between risk measures and acceptance sets in the case of such an eligible asset. It is well-known that risk measures corresponding to general eligible assets are not necessarily finitely valued and continuous. Therefore, we study how the choice of the eligible asset, i.e. whether it follows a discrete or a continuous probability distribution, influences the corresponding risk measures. We focus on the finiteness and continuity properties of these risk measures. Our investigation is complemented with frequently used acceptability criteria, namely the Value-at-Risk- and the Expected Shortfall-acceptability. The theory of general risk measures allows for a wider range of eligible assets. Hence, we investigate the influence of concrete choices of general eligible assets, i.e. defaultable bonds and call options. Our results show that the finiteness and continuity properties of general risk measures can depend on the probability distribution of the corresponding eligible assets. Therefore, it is important to distinguish between discrete and continuous eligible assets. |
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