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20 - Transition Modeling

from IV - Longitudinal Modeling

Published online by Cambridge University Press:  05 August 2014

By
Bruce Jones  and
Weijia Wu
Edited by
Edward W. Frees ,
Richard A. Derrig  and
Glenn Meyers
Bruce Jones
Affiliation:
University of Western Ontario
Weijia Wu
Affiliation:
University of Southern California
Edward W. Frees
Affiliation:
University of Wisconsin, Madison
Richard A. Derrig
Affiliation:
Temple University, Philadelphia
Glenn Meyers
Affiliation:
ISO Innovative Analytics, New Jersey
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Summary

Chapter Preview. This chapter provides an introduction to transition modeling. 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 on 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 flow 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 – only basic probability and statistics as well as life contingencies – is minimal.

Type
Chapter
Information
Predictive Modeling Applications in Actuarial Science , pp. 515 - 538
Publisher: Cambridge University Press
Print publication year: 2014

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References

Aalen, O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics 6(4), 701–726.CrossRefGoogle Scholar
Andersen, P. K. (1993). Statistical Models Based on Counting Processes. Springer, New York.CrossRefGoogle Scholar
Andersen, P. K. and N., Keiding (2002). Multi-state models for event history analysis. Statistical Methods in Medical Research 11(2), 91–115.CrossRefGoogle ScholarPubMed
Cox, D. D. R. and D., Oakes (1984). Analysis of Survival Data, Volume 21. CRC Press, Boca Raton, FL.Google Scholar
Dickson, D. C., M. R, Hardy, and H. R, Waters (2009). Actuarial Mathematics for Life Contingent Risks. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Haberman, S. and E., Pitacco (1999). Actuarial Models for Disability Insurance. CRC Press, Boca Raton, FL.Google Scholar
Hoem, J. M. (1969). Markov chain models in life insurance. Blätter der DGVFM 9(2), 91–107.CrossRefGoogle Scholar
Kalbfleisch, J. D. and R. L, Prentice (2002). The Statistical Analysis of Failure Time Data (2nd ed.). John Wiley & Sons, New York.CrossRefGoogle Scholar
Klugman, S. A., H. H, Panjer, and G. E, Willmot (2012). Loss Models: From Data to Decisions (4th ed.), Volume 715. John Wiley & Sons, New York.Google Scholar
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data (2nd ed.). John Wiley & Sons, New York.Google Scholar
Macdonald, A. (1996a). An actuarial survey of statistical models for decrement and transition data-i: Multiple state, Poisson and binomial models. British Actuarial Journal 2(1), 129–155.Google Scholar
Macdonald, A. (1996b). An actuarial survey of statistical models for decrement and transition data: II: Competing risks, non-parametric and regression models. British Actuarial Journal, 429–448.Google Scholar
Macdonald, A. S., H. R, Waters, and C. T, Wekwete (2005a). A model for coronary heart disease and stroke with applications to critical illness insurance underwriting I: The model. North American Actuarial Journal 9(1), 13–40.Google Scholar
Macdonald, A. S., H. R, Waters, and C. T, Wekwete (2005b). A model for coronary heart disease and stroke with applications to critical illness insurance underwriting II: Applications. North American Actuarial Journal 9(1), 41–56.Google Scholar
Nelson, W. (1969). Hazard plotting for incomplete failure data. Journal of Quality Technology 1(1).CrossRefGoogle Scholar
Norberg, R. (1995). Differential equations for moments of present values in life insurance. Insurance: Mathematics and Economics 17(2), 171–180.Google Scholar
Ramlau-Hansen, H. (1988). The emergence of profit in life insurance. Insurance: Mathematics and Economics 7(4), 225–236.Google Scholar
Waters, H. R. (1984). An approach to the study of multiple state models. Journal of the Institute of Actuaries 111(2), 363–374.CrossRefGoogle Scholar

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