Systemic Trade Collapse Probability under Compounded Geopolitical Shocks: A Max-Stable Process Approach with Bivariate H\"{u}sler-Reiss Spectral Density for the Trump Tariff Regime and Iran Conflict

Abstract Classical approaches to modeling geopolitical trade shocks treat them as additive perturbations to a fundamentally stable system. The simultaneous imposition of sweeping US tariff regimes under the Trump administration and escalating military pressure on Iran expose the inadequacy of this assumption at a historically consequential scale. These are not perturbations. They are correlated tail events whose joint dependence structure in the extremes differs qualitatively from their center-of-distribution behavior, and modeling them additively systematically underestimates the probability of catastrophic multi-corridor trade collapse. We develop a formal framework for the systemic trade collapse probability $\TCEP(\lambda_T, \lambda_I, \Gamma, u)$, defined as the probability that $d \geq 2$ critical bilateral corridors simultaneously fall below threshold fraction $u$ of pre-shock volumes. The framework is grounded in max-stable process theory with a bivariate H"{u}sler-Reiss spectral density characterizing tail dependence between tariff-induced and conflict-induced disruptions. Joint shock arrivals are modeled as a bivariate marked Hawkes process with a shared CIR intensity component. The TCEP admits a closed-form expression, and the risk amplification factor \begin{equation*} \mathcal{A}(\Gamma, u) = \frac{\TCEP(\lambda_T, \lambda_I, \Gamma, u)} {\TCEP(\lambda_T, 0, \Gamma, u) + \TCEP(0, \lambda_I, \Gamma, u)}\end{equation*} exceeds unity for all $\Gamma < \infty$, with amplification strictly increasing as tail dependence strengthens. Empirical estimation from bilateral trade flow data during the 2018 US-China tariff war and the 2019 Strait of Hormuz crisis yields $\hat{\Gamma} = 1.84$ with 95\% confidence interval $[1.31, 2.47]$, corresponding to $\hat{\mathcal{A}} = 2.13$ at the 10\% collapse threshold: the compound shock is more than twice as dangerous as either shock alone. Sensitivity analysis across fifteen systemic corridors identifies Hormuz-dependent routes as the dominant systemic risk nodes. Policy implications for reserve management, trade diversification, and multilateral coordination are developed. MSC 2020: 60G70, 62G32, 62P20, 91B84. JEL Classification: C58, F13, F51, F52, G15.