Pricing multi-peril agricultural insurance under compound climate hazards demands a framework that captures stochastic dependence among heterogeneous perils, accommodates non-stationary loss dynamics, and supports adaptive policy optimisation. We demonstrate that backward stochastic differential equations, combined with copula dependence, recurrent neural networks, and reinforcement learning, provide a unifying language for this task; the contribution lies in their principled integration. The dynamic premium is the unique adapted solution of a BSDE whose driver encodes compound-risk dependence through a Student-t copula, forward loss dynamics through a jump-diffusion process, and a green-finance adjustment through an optimal control variable. Within this framework we derive three progressive results by adapting standard BSDE theory to the compound-dependence and policy-control setting. First, existence and uniqueness hold under Lipschitz and square-integrability conditions. Second, a comparison theorem guarantees that a larger correlation matrix yields higher premiums; the degrees-of-freedom effect enters separately through the risk-loading magnitude. Third, the Euler discretisation converges at a rate of one half of the time-step size, with copula estimation, LSTM conditional expectation approximation, and Q-learning HJB solution as sequential components. Applied to eleven Zhejiang cities (2014–2023, N × T=110), in this illustrative application the framework reduces premium variance by 43.5 percent (bootstrap 95% CI: 38.2%,48.7%) while maintaining actuarial adequacy with a mean loss ratio of 0.678, though the modest sample size warrants caution in generalising these findings. Each component contributes statistically significant improvements confirmed by the Friedman test at the 0.1 percent significance level.
Pei et al. (Thu,) studied this question.