Predictive Modeling Applications in Actuarial Science

Chapter 8 - The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon


Glenn Meyers

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This chapter shows how to take the output of a Bayesian MCMC stochastic loss reserve model and calculate the predictive distribution of the estimates of the expected loss over a nite time horizon. Then given a 99.5% VaR regulatory capital requirement, it shows how to calculate the regulatory capital for a one-, two-, and three-year time horizon.

As an insurer gathers more data on its loss development in subsequent calendar years, this chapter finds that in most cases, it can release capital to its investors over time. But in other cases it will have to add capital in subsequent years. In keeping with the 99.5% VaR criterion, it finds that for many insurers, this additional capital can be substantial. As capital becomes more expensive to the stressed insurer, it might be prudent capital management for an insurer to voluntarily raise that capital in advance. This chapter shows one way to calculate the amount of voluntary capital that will be needed to satisfy the 99.5% VaR requirement for the next calendar year.