Risk aggregation and Fréchet problems
Prof. Dr. Ruodu Wang (University of Waterloo)
Dates and times
October 12, 2015, 13:15 - 15:00
October 14, 2015, 13:15 - 15:00
October 16, 2015, 13:15 - 15:00
October 26, 2015, 13:15 - 15:00
October 28, 2015, 13:15 - 15:00
Place
HG G 19.1
Abstract
Fréchet problems refer to questions related to an aggregation (sum, typically) of several random variables, where the marginal distribution of each individual random variable is known and the joint distribution (copula) is unspecific. Unfortunately (in fact, fortunately), a large number of questions in this field are still mathematically open.
In the modeling of risk aggregation, individual risks and their dependence structure are often modeled separately, leading to uncertainty arising at the level of a joint model. As the dependence structure is typically uncertain, the study on quantitative characteristics (e.g. risk measures) of risk aggregation under model uncertainty leads to a variety of Fréchet problems.
This course covers various topics in this quickly expanding field. The content is mainly based on recent research of the instructor and his collaborators.
Tentative topics:
1) Introduction to Fréchet problems
2) Copulas and extremal dependence concepts
3) Complete and joint mixability
4) Dependence uncertainty for sequences
5) Risk aggregation, risk measures and bounds
6) Numerical methods
7) Partial dependence information
8) Open questions
Some references:
[1] Wang, B. and Wang, R. (2015). Joint mixability. Mathematics of Operations Research, forthcoming.
[2] Puccetti, G. and Wang, R. (2015). Extremal dependence concepts. Statistical Science, forthcoming.
[3] Embrechts, P., Wang, B. and Wang, R. (2015). Aggregation-robustness and model uncertainty of regulatory risk measures. Finance and Stochastics, forthcoming.
[4] Wang, R. (2014). Sum of arbitrarily dependent random variables. Electronic Journal of Probability, 19(84), 1-18.
[5] Embrechts, P., Puccetti, G., Rüschendorf, L., Wang, R. and Beleraj, A. (2014). An academic response to Basel 3.5. Risks, 2(1), 25-48.
[6] Embrechts, P., Puccetti, G. and Rüschendorf, L. (2013). Journal of Banking and Finance, 37(8), 2750-2764.