# 401-3958-14L Risk Measures

Semester | Frühjahrssemester 2014 |

Dozierende | V. Bignozzi |

Periodizität | einmalige Veranstaltung |

Lehrsprache | Englisch |

Kurzbeschreibung | The aim of the course is to present an overview of risk measures available in the academic literature or currently used in practice emphasizing their properties and drawbacks. Students will then be familiar with VaR, Expected shortfall, coherent and convex risk measures and the recent expectiles. The course will also discuss practical issues arising from estimating and backtesting risk measures. |

Lernziel | Risk measures are important tools for managing and quantifying financial and insurance risks. The aim of the course is to present an overview of different kind of risk measures available in the academic literature or currently used in practice emphasizing their properties and drawbacks. Students will then be familiar with VaR, Expected shortfall, coherent and convex risk measures but also with the more recent expectiles. The last part of the course will discuss practical issues arising from estimating and backtesting risk measures. |

Inhalt | -Introduction to monetary risk measures and their use in finance and actuarial science; -VaR: definition, examples and drawbacks; -Expected shortfall and distorted risk measures:coherency and comotonicity; -Robust representation of coherent and convex risk measures; -Shortfall risk measures: the entropic risk measure and expectiles; -Law-invariant risk measures and their definition on probability distribution spaces; -Forecasting and backtesting of a risk measure. |

Skript | Please check the website http://www.math.ethz.ch/education/bachelor/lectures/fs2014/math/risk_measures |

Literatur | For further reading we recommend: BOOKS: H. Föllmer, A. Schied (2011). Stochastic Finance: An Introduction in Discrete Time. de Gruyter. M. Denuit, J. Dhaene, M. Goovaerts and R. Kaas (2005). Actuarial Theory for Dependent Risks. Measures, Orders and Models. Wiley. A. J. McNeil, R. Frey and P. Embrechts (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press. P. Jorion (2007). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw Hill. PAPERS: P. Artzner, F. Delbaen, J. M. Eber, D. Heath (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-228. Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. Frittelli, M., & Rosazza Gianin, E. (2002). Putting order in risk measures. Journal of Banking & Finance, 26(7), 1473-1486. Tasche, D. "Risk measures: Yet another search of a holy grail." (2013). |

Voraussetzungen / Besonderes | Basic course in probability theory and mathematical statistics |