INCORPORATING SPATIAL CORRELATION IN PROBABILISTIC LOSS ASSESSMENT: AN IMPROVED CONVOLUTION-BASED METHOD WITH A CASE STUDY

Catastrophic risk management requires a comprehensive understanding of aggregate loss distribution, as well as an in-depth knowledge of the uncertainties influencing the reliability of this distribution. Aggregate loss distribution is particularly sensitive to uncertainties arising in hazard assessment processes and the vulnerability of building typologies. Traditionally, simulation-based methods are employed to estimate and analyze aggregate loss distribution, as these methods enable the modelling of complex uncertainties in hazard exposure and vulnerability. However, simulation-based approaches come with notable limitations: they are computationally intensive and time-consuming, particularly when analyzing large asset portfolios and attempting to calculate the tail of the loss distribution. Therefore, an alternative framework is proposed to calculate aggregate loss distribution using a convolution-based approach grounded in the total probability theorem. This framework is further enhanced by incorporating spatial correlation in intra-event shaking intensity, which is crucial for calculating aggregate loss in low exceedance probabilities for large portfolios. The improved convolution-based and simulation-based methods are applied to a portfolio in Zeytinburnu, Istanbul. The results demonstrate that the improved convolution-based method not only provides a more computationally efficient method but also offers more reliable aggregate loss in the tails of the distribution compared to the conventional simulation-based method. This framework offers a valuable tool for enhancing decision-making in risk transfer and mitigation efforts.