Climate change and weather risk affect economy and livelihood over large scales, especially for agricultural production which depends on weather conditions. For example, United States Department of Agriculture estimates that 70-90\% of agricultural production loss can be attributed to adverse weather. In practice, weather index insurance can be employed to hedge against weather risk. The payoff of weather index insurance is exclusively based on some prespecified weather indices instead of the actual losses incurred to the insureds. Hence it avoids the high administration costs, adverse selection and moral hazard issues associated with conventional indemnity-based insurance. While promising, current index insurance faces low demand due to the large basis risk, the risk that the underlying indices and actual losses are mismatched.

We aim to reduce the basis risk in several ways. First, crop production depends on high-dimensional weather conditions. We should carefully select and include a sufficiently large number of weather variables when constructing the insurance contract. Second, due to biological reasons, crop production depends on weather conditions in a highly nonlinear way. Tapping into recent advances in machine learning, we propose a neural network-based index insurance design. Specifically, we embed a neural network-based scheme into an expected utility maximization problem with budget constraints to capture farmers’ insurance demand. Neural networks capture highly nonlinear relationship between the high-dimensional weather variables and production losses. We endogenously solve for the optimal insurance premium and demand to incorporate strategic interaction between farmers and insurers. Our neural network-based index insurance reduces basis risk, lowers insurance premium, and improves farmers' utility.