Balancing Public and Private Interests in Urban Transformations: Handling Uncertainty with the Monte Carlo Method

Urban transformations require balancing private real estate interests with the provision of public spaces that enhance sustainability and ecosystem services. This study proposes a probabilistic model to assess the feasibility of transforming buildable areas while ensuring equitable benefits for both private developers and public administrations, with a focus on three areas to be regenerated within the Municipality of Lucca as case studies. Applying the Monte Carlo (MC) method, two probabilistic models—one with a Uniform distribution and the other with a Normal distribution—estimate the expected Transformation Value (TV) and its associated uncertainty. Results highlight the effectiveness of MC-based assessments in managing financial uncertainty, aiding developers in risk evaluation, and supporting policymakers in designing balanced urban planning indices. It was observed that the Uniform model is better suited to situations in which the initial values of the model’s main variables—such as construction costs, post-transformation market value, or transformation duration—are not fully known, whereas the Normal model provides more accurate estimates when the investment scenario is better understood. The results demonstrate that this approach provides, on the one hand, a robust tool for investment risk analysis to private investors and, on the other hand, a way for public institutions to verify whether urban planning indices enable private promoters to contribute effectively to the development of sustainable cities.