Develop interaction mechanisms beyond joint exchangeability

Develop interaction mechanisms for modeling interactions in collective insurance loss processes that do not rely on joint exchangeability of arrays—i.e., invariance of the joint distribution of the infection/transmission array I=(I_{i,j}) and the conditional loss expenditure array Z=(Z_{i,j}) under permutations of vertices—so that dependence structures in losses can be specified and analyzed without the jointly exchangeable assumption.

Background

The paper models systemic risk in insurance portfolios using jointly exchangeable arrays to represent infections/transmissions (I) and conditional loss expenditures (Z), with realized losses G defined by G_{i,j}=I_{i,j}·Z_{i,j}. Joint exchangeability provides a tractable invariance structure under vertex permutations, enabling ergodic decompositions and central limit theorems for total losses.

In the conclusion, the authors explicitly identify a need to go beyond this symmetry class. Developing interaction mechanisms not restricted to joint exchangeability would allow richer dependence structures (e.g., non-exchangeable, locally interacting, or time-evolving networks) and could broaden applicability to more realistic contagion and systemic settings.