Robust Risk Aggregation: Theory and Applications
Modeling inter-dependence among multiple risks often faces statistical as well as modeling challenges, with considerable uncertainty arising naturally. This issue is crucial in modern risk management and regulation regimes in banking and insurance. To deal with the uncertainty at the level of dependence in multivariate models, various techniques in robust risk aggregation have been developed in the past few years. First, I will review some recent developments and open challenges in the field. Then, I will discuss an application of robust risk aggregation: merging p-values in multiple hypothesis testing, a classic problem in statistical theory. It turns out that recent results in robust risk aggregation can be utilized to establish various conservative and precise averaging methods of p-values. For instance, we show that K p-values can be combined by scaling up their arithmetic mean by a factor of 2, their geometric mean by a factor of e, or their harmonic mean by a factor of e(logK). This gives an interesting example where mathematical techniques developed in quantitative risk management and actuarial science are found tremendously useful to another major scientific field.