Bikramjit Das (Singapore University of Technology and Design)
Multivariate regular variation on different Euclidean cones have been used to understand various kinds of tail risks. In this talk we explore risk assessment in two such related settings. Our first setting is of bipartite networks with heavy-tailed risk factors. As an example consider the risk of ruin, insolvency or large losses in an insurance company with multiple business lines. We assess large loss event for such a company which 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. For our second setting we look at iid sums of such heavy-tailed claims and assess tail risk events as mentioned above. We also explore finite time ruin problems in this setting. We show in both settings that under an assumption of multivariate regular variation on the joint distribution of claims, we can compute the risk of a variety of such risk and ruin events with relative ease.
The talk is based on the paper [1] and an on-going work [2].
[1] B.Das, V. Fasen-Hartmann and C. Klüppelberg, Tail probabilities of random linear functions of tail probabilities of regularly varying random vectors. Extremes (2022+).
[2] B. Das, and V. Fasen-Hartmann, Aggregating heavy-tailed vectors: tail risk and ruin (forthcoming).