Predictive Modeling Applications in Actuarial Science

Chapter 20 - Transition Modeling


Bruce Jones | University of Western Ontario

Weijia Wu | University of Western Ontario

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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 multi-state 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 multi-state 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 multi-state 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 multi-state 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.