Large Language Models (LLMs) are increasingly deployed as autonomous agents for simulation and decision-making, necessitating a deeper understanding of their decision-making behaviour under risk. We investigate the relationship between LLMs’ personality traits and risk-propensity, applying Cumulative Prospect Theory (CPT) and the Big Five personality framework. We compare the behaviour of several LLMs to human baselines. Our findings show that the majority of the models investigated are risk-neutral rational agents, whilst displaying higher Conscientiousness and Agreeableness traits, coupled with lower Neuroticism. Interventions on Big Five traits, particularly Openness, influence the risk-propensity of several LLMs. Advanced models mirror human personality-risk patterns, suggesting that cognitive biases can be surfaced by optimal prompting. However, their distilled variants show no cognitive bias, suggesting limitations to knowledge transfer processes. Notably, Openness emerges as the most influential factor to risk-propensity, aligning with human baselines. In contrast, less advanced models demonstrate inconsistent generalization of the personality-risk relationship. This research advances our understanding of LLM behaviour under risk and highlights the potential and limitations of personality-based interventions in shaping LLM decision-making.