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

In this talk we discuss the problem of assessing the risk related to time. On one hand, classical regulatory rules for capital allocation of long-tailed insurance risks do not ask insurance companies to hold solvency capital early in the process. However, this may underestimate the risk of a deterioration of the credit state of the company until the time when the capital is needed. On the other hand, actually implemented actuarial capital management strategies of companies can often be interpreted as implicitly allocating that capital earlier than demanded. We propose a framework for quantifying risks associated with time and model the impact of exogenous credit migration risk as well as the financial repercussions of overlooking it. We evaluate six different strategies, including the costs associated with potential company bankruptcy until the settlement of long-term claims, and detail the practical implications for a numerical implementation of a heavy-tailed insurance risk anticipated in the future. This is joint work with Michel Dacorogna.

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