A stochastic framework for ruin probabilities under time-changed Brownian motion

This study investigates ruin probabilities in the insurance sector using a time-changed Brownian motion framework. By incorporating a normal inverse Gaussian (NIG) process, the model overcomes the limitations of traditional models with deterministic time evolution. The proposed approach introduces a stochastic time component governed by an inverse Gaussian process, allowing a more flexible and realistic assessment of ruin probabilities. We also extend the model by incorporating reinsurance mechanisms, offering a comprehensive view of risk allocation. The results highlight the model’s robustness and practical relevance in both insurance and reinsurance contexts, contributing to the literature on advanced risk processes.