Predictive Modeling Applications in Actuarial Science
 Volume 1
 Introduction
 Predictive Modeling Foundations
 Predictive Modeling Methods
 Bayesian and Mixed Modeling
 Longitudinal Modeling
 Volume 2
 Generalized Linear Model
 Extensions of the Generalized Linear Model
 Unsupervised Predictive Modeling Methods

Applications on Current Problems in Actuarial Science
 Chapter 8  The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
 Chapter 9  Finite Mixture Model and Workersâ€™ Compensation LargeLoss Regression Analysis
 Chapter 10  A Framework for Managing Claim Escalation Using Predictive Modeling
 Chapter 11  Predictive Modeling for UsageBased Auto Insurance
Chapter 8  The Predictive Distribution of Loss Reserve Estimates over a Finite Time Horizon
Authors
Glenn Meyers
ggmeyers@metrocast.net
Chapter Preview
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 threeyear 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.