Speaker: Bikram Das, SUTD
We create a framework for studying risk in bipartite networks with heavy-tailed risk factors. As as example consider the risk of ruin, insolvency or large losses in an insurance company with multiple business lines. Insurance claims are often modeled using heavy-tailed distributions and each business line gets affected by a set of such claims. Ruin, or a large loss event for such a company may occur in a variety of ways depending on the definitions and rules set up by the company: it may occur due to one, or two, or a subset, or a linear combination of the business lines incurring large losses. We model such risk using a bipartite network structure and show that under an assumption of multivariate regular variation on the joint distribution of claims, we can compute the risk of a variety of such ruin events with relative ease. Incidentally, classical models are often unable to compute such probabilities or may report the probabilities to be zero.Our work also provides a multivariate extension of the so-called Breiman’s theorem on tail behaviour of a product of random variables.
The seminar is based on the paper "Tail probabilities of random linear functions of tail probabilities of regularly varying random vectors" (B.Das, V. Fasen-Hartmann and C. Klüppelberg) and an on going work in collaboration with Vicky Fasen-Hartmann and Claudia Klüppelberg.