Geopolitical risk perception and the value of waiting: A real options model with Bayesian learning

This paper develops a continuous-time real options model with Bayesian learning to analyze how geopolitical risk perception (GRP) affects corporate investment. We model GRP as a latent state following a hidden Markov process, requiring managers to infer the regime from an exogenous, noisy cash flow signal. By solving the filtering problem and the corresponding investment timing problem, we show that Bayesian learning generates a “fog of war” effect where investment thresholds peak not at certainty, but under maximum ambiguity. We quantify a “belief scarring” mechanism where subjective beliefs recover slowly after crisis resolution, causing a persistent l-shaped investment recovery. Simulation results indicate that perceptual frictions generate an average cumulative capital misallocation of about 42.13 units per firm, representing about 4.21% of the baseline investment scale, which is heavily concentrated in transition periods. Our findings suggest that the subjective interpretation of geopolitical events is as critical as the events themselves in shaping the global macroeconomic landscape.