Climate-Conditioned Cascade Modeling for Multi-Peril Reinsurance: Analysis and Controlled Numerical Applications

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.