Analysis of Abnormal Variations in Pedestrian Flow Intensity and Probabilistic Estimation of Retail Profit–Loss Risk in Urban Commercial Clusters Using Poisson Jump Processes and Monte Carlo Stochastic Simulation

Abstract

Pedestrian-flow fluctuations in urban commercial clusters directly affect customer exposure and short-term operating risk, yet conventional count and time-series models often absorb abrupt changes into residual variation and remain disconnected from probabilistic retail-loss assessment. This study develops a seasonally adjusted compound Poisson jump framework coupled with Monte Carlo risk propagation to distinguish recurrent pedestrian intensity from discrete abnormal changes and translate flow shocks into conditional shop-level profit–loss risk. Hourly pedestrian counts and spatial business-establishment data from Melbourne are synchronized to estimate baseline intensity, jump frequency, signed magnitude, and decay, after which uncertain conversion rates, transaction values, margins, and fixed costs are propagated through 100,000 Monte Carlo paths. On the 2024 out-of-sample evaluation period, the proposed model reduced MAE by 8.3%, negative log-likelihood by 3.9%, and CRPS by 7.4% relative to the strongest benchmark, with all differences significant at the 5% level. The pooled operating-loss probability increased from approximately 0.23 under regular conditions to 0.38 under negative-jump states, while normalized 95% CVaR increased from 0.78 to 1.17 fixed-cost units under strong negative shocks. At 100,000 paths, the Monte Carlo standard error was approximately 0.0015. These results link interpretable pedestrian-flow discontinuities with uncertainty-aware retail risk measures and support probabilistic assessment of commercial exposure under abnormal urban-flow conditions.