Allocating Capital to Time: Introducing Credit Migration for Measuring Time-Related Risks

Assessing time-related risks in long-tailed insurance is challenging. Regulatory capital allocation rules may underestimate credit deterioration risk by not requiring insurers to hold solvency capital early, while actuarial practices often allocate capital sooner than mandated. We propose a framework to quantify these time-associated risks and evaluate capital allocation strategies based on time to ultimate, aiming to manage long-tail business effectively. By modeling the impact of exogenous credit migration risk, we evaluate six strategies, including costs associated with potential company bankruptcy until long-term claims are settled. Using a numerical example of a future heavy-tailed insurance risk, we estimate a Markov chain credit migration model with insurance market data and analyze liability values from various capital management strategies. Our findings show that early capital raising is costly, even with penalties for avoided credit risk, unless the company's initial credit rating is poor. In such cases, purchasing protection through a credit derivative may be more efficient, if available.