🤖 AI Summary
Traditional joint loss models struggle to capture the temporal dependencies and state-dependent propagation among climate hazards, leading to biased reinsurance risk assessments. This work proposes a Cascading Climate Risk Network (CCRN) that decouples annual-scale climatic conditions from intra-event propagation mechanisms using a directed acyclic graph. The model maps physical states to insurance losses through a complementary log-log triggering function, bounded severity activation, and a capacity-constrained demand surge transformation. It innovatively derives a path-dependent closed-form solution for cascading losses and constructs pathwise upper-bound losses over rectangular stress sets, enabling transparent, contract-level stress testing. Numerical experiments, conducted for the first time in a synthetic environment, confirm that directional propagation critically shapes tail risk, identifying directional propagation, annual event frequency, and dependency strength as the three key drivers. Mid-layer reinsurance pricing proves robust to marginal dependency structures, whereas upper-tail behaviors exhibit significant divergence.
📝 Abstract
Climate perils are linked through event ordering and state-dependent propagation, features not fully captured by joint loss distributions alone. This paper develops a Cascading Climate Risk Network (CCRN) for multi-peril reinsurance that separates calendar-scale climate conditioning from within-event propagation on a directed acyclic graph (DAG). The model combines complementary-log-log triggering hazards with bounded severity activation, mapping physical states to insured losses via a capacity-bounded demand-surge transformation.
For fixed shocks, the event-scale cascade reaches a unique finite-step closure. Monotone comparative statics provide a pathwise upper-corner loss bound over rectangular stress sets, yielding a transparent contract-level stress-testing guarantee under common aleatory inputs.
Comprehensive numerical experiments, including copula and Bayesian-network benchmarks, sensitivity analyses, and uncertainty propagation, demonstrate that while central layer prices remain robust across matched-marginal dependence structures, far-tail and high-layer behaviors differ materially. Directional propagation, annual event frequency, and dependence strength emerge as the principal risk drivers. The study provides a controlled synthetic verification of the proposed architecture.