Risk-based optimization of investment planning for built cultural heritage conservation

The progressive contraction of public funding has made the use of private sponsorship increasingly important for financing the conservation of historical and architectural heritage. This tool not only ensures the conservation of assets but also acts as a reputational lever for companies. However, literature rarely provides integrated models capable of guiding investment decisions by indicating how much to invest in sponsorship, how to allocate resources over time, and which level of risk to accept. This paper proposes an innovative approach that combines two components. The first is a dynamic optimization system, based on the Cobb–Douglas production function and Lagrange multipliers, identifying the annual investment that maximizes the present value of future profits for the sponsoring company. The second is a Monte Carlo-based risk assessment protocol, enabling the estimation of the probability of financial failure of the sponsorship campaign and the assessment of the overall sustainability of the operation. The model is applied to a real case study involving a large international company engaged in multi-year sponsorship programs for heritage restoration in Italy. Results indicate that optimized investment planning can generate long-term financial benefits, while also revealing a non-negligible probability of financial failure, even under optimal conditions. This finding highlights the importance of incorporating risk-aware strategies into cultural sponsorship decisions. The study offers contributions on several levels. Concerning research, it fills a methodological gap in the field of cultural sponsorship. Regarding practice, it provides sponsoring companies with a transparent and replicable tool to effectively estimate monetary returns and cultural institutions with support to strengthen project credibility in the sustainable planning of conservation investments. Finally, on a social level, it promotes greater transparency in public-private partnerships and a more efficient use of resources allocated to heritage.