Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa2-748461
Schlotter, Ruben
Shapiro, Alexander ; Benth, Fred Espen (Gutachter)
Contributions to the theory of dynamic risk measures
Kurzfassung in englisch
This thesis aims to fill this gap between static and dynamic risk measures. It presents a theory of dynamic risk measures based directly on classical, static risk measures. This allows for a direct connection of the static, the discrete time as well as the continuous time setting. Unlike the existing literature this approach leads to a interpretable pendant to the well-understood static risk measures. As a key concept the notion of divisible families of risk measures is introduced. These families of risk measures admit a dynamic version in continuous time. Moreover, divisibility allows the definition of the risk generator, a nonlinear extension of the classical infinitesimal generator. Based on this extension we derive a nonlinear version of Dynkins lemma as well as risk-averse Hamilton–Jacobi–Bellman equations.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Finanzmathematik | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Pichler, Alois | |
| SWD-Schlagwörter: | Stochastik , Dynamische Optimierung | |
| Freie Schlagwörter (Englisch): | risk-aversion , dynamic risk measures , continuous time , Black-Scholes | |
| DDC-Sachgruppe: | Mathematik | |
| Sprache: | englisch | |
| Tag der mündlichen Prüfung | 03.05.2021 | |
| OA-Lizenz | CC BY 4.0 |
