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 20  Transition Modeling
Authors
Bruce Jones  University of Western Ontario
jones@stats.uwo.ca
Weijia Wu  University of Western Ontario
Chapter Preview
This chapter provides an introduction to transition modeling. To understand what this is, consider a situation where an individual or entity is, at any time, in one of several states and may from time to time move from one state to another. The state may, for example, indicate the health status of an individual, the status of an individual under the terms of an insurance policy, or even the "state" of the economy. The changes of state are called transitions. There is often uncertainty associated with how much time will be spent in each state and which state will be entered upon each transition.
This uncertainty can be modeled using a multistate stochastic model. Such a model may be described in terms of the rates of transition from one state to another. Transition modeling involves the estimation of these rates from data.
Actuaries often work with contracts involving several states and financial implications associated with presence in a state or transition between states. A life insurance policy is a simple example. A multistate stochastic model provides a valuable tool to help the actuary analyze the cash ow structure of a given contract. Transition modeling is essential to the creation of this tool.
This chapter is intended for practitioners, actuaries or analysts who are faced with a multistate setup and need to estimate the rates of transition from available data. The assumed knowledge is minimal, only basic probability and statistics as well as life contingencies.
Following a discussion of some relevant actuarial applications in Section 20.1, this chapter gives a brief introduction to multistate stochastic models in Section 20.2. We follow the notation, terminology, and approach of (Dickson et al., 2009, chapter 8). While our introduction is intended to stand on its own, the reader is encouraged to consult Dickson et al. (2009) for a more detailed presentation. Once multistate models have been introduced, we discuss how to estimate the rates of transition under different assumptions about the model and the data. This is presented in Sections 20.3 and 20.4.