This paper analyzes the risks in random sets and their implications for basket derivatives. Based on an extension of integration by parts for random set, we define stochastic dominance of order 1 and 2 for random sets. Since the ordering of sets, that is the inclusion, is a partial order, we...

The ultra long run (ULR) discount rates are key inputs for valuing pension funds, life annuities, or firms with long run investments due to low carbon transition. However the corresponding zero-coupon bonds are only actively traded up to a last liquid point (LLP) such as 20 years, say. This...

Whereas data on return volatilities are available for a large number of assets, this is less frequently the case of covolatilities. We introduce an approach based on static and dynamic Wishart models to solve this problem of missing data. We first discuss the identification of the parameter of...

One of the objectives of the recent prudential regulation is to separate the computation of required capital for short- and long-run risks. This paper provides a coherent framework to define, compute, and update these components. We provide different examples, among which is the transition to...