Stochastic optimization via GARCH-Cox hazard modeling to mitigate agricultural SME failure in emerging economies

Abstract

Extant financial distress models, developed predominantly in high-income, low-volatility contexts, fail to capture the compound exposure of smallholder agribusinesses to simultaneous commodity price shocks and climatic disruption. We address this theoretical gap by developing a stochastic survival optimization framework that integrates a GARCH(1,1)–GJR conditional variance model with a time-varying Cox Proportional Hazard specification, formally embedding heteroskedastic agroclimatic risk into the failure probability function. Using longitudinal panel data from 205 agricultural SMEs registered with the Superintendencia de Compañías del Ecuador in Quevedo — Los Ríos, a region whose banana and cacao cycles exhibit price-support volatility exceeding 34% annualized standard deviation—we estimated a discriminant survival model across 80 sampled firms (2021–2025). The theoretical equilibrium, derived via Karush–Kuhn–Tucker (KKT) optimality conditions, yields a critical leverage threshold (Zoc = −0.2263) and a portfolio diversification boundary (σ* = 0.312) below which failure probability rises nonlinearly. Empirically, 43 of 80 firms (53.75%) operate in the high-failure zone, with conditional failure hazard increasing by 2.14 per unit decline in retained-earnings ratio. Our framework provides agrifood policymakers and SME managers with actionable threshold-based decision rules calibrated to the institutional context of Los Ríos. Beyond the Ecuadorian case, the model constitutes a generalizable contribution to survival analysis under non-Gaussian financial conditions.