Flood insurance is an effective strategy for individuals to mitigate disaster-related losses. However, participation rates among at-risk populations in the United States remain strikingly low. This gap underscores the need to understand and model the behavioral mechanisms underlying insurance decisions. Large language models (LLMs) have recently exhibited human-like intelligence across wide-ranging tasks, offering promising tools for simulating human decision-making. This study constructs a benchmark dataset to capture insurance purchase probabilities across factors. Using this dataset, the capacity of LLMs is evaluated: while LLMs exhibit a qualitative understanding of factors, they fall short in estimating quantitative probabilities. To address this limitation, InsurAgent, an LLM-empowered agent comprising five modules including perception, retrieval, reasoning, action, and memory, is proposed. The retrieval module leverages retrieval-augmented generation (RAG) to ground decisions in empirical survey data, achieving accurate estimation of marginal and bivariate probabilities. The reasoning module leverages LLM common sense to extrapolate beyond survey data, capturing contextual information that is intractable for traditional models. The memory module supports the simulation of temporal decision evolutions, illustrated through a roller coaster life trajectory. Overall, InsurAgent provides a valuable tool for behavioral modeling and policy analysis.