The increasing prevalence and heightened severity of extreme weather events, which are consequences of climate change, pose significant challenges to the global property insurance sector. This study examines the concurrent crises faced by insurance companies in maintaining profitability and by property owners in affording coverage, thereby necessitating a reevaluation of current insurance paradigms. We present an innovative approach that utilizes a back-propagation (BP) neural network to forecast insurance losses and guide strategic underwriting decisions in regions prone to perils. Our advanced model combines crucial factors such as the likelihood of extreme meteorological phenomena, insurance risk premiums, and capital adequacy ratios to predict impending losses and inform insurance policy formulation. Through an extensive analysis of nearly two decades of catastrophe data from the United States and New Zealand, we determine the model's effectiveness in anticipating insurance-related losses and providing strategic guidance to insurance entities. The study concludes with recommendations for insurers to enhance risk assessment, innovate products, collaborate with governments, invest in green projects, and establish dedicated climate risk management teams. The study contributes to the discourse on climate change adaptation in the insurance industry and offers practical solutions for navigating the complexities of extreme weather risk.