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092009 (M10) Bayesian methods in actuarial science
142
Abstractsand Reviews
Process Models MacDonald A.S., British Actuarial Journal, Nr. 2,
1996, 703-726 Counting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial eduction is discussed. Keywords: Censoring, Compensators, Counting processes, Kaplan-Meier estimate, Martingales, Multiple state models, Nelson-Aalen estimate, Partial likelihood, Survival Analysis. 092007 (M10) The Modelling of Recent Mortality Trends in United Kingdom Male Assured Lives Renshaw A.E., Haberman S., Hatzopoulos P., British
Actuarial Journal, Nr. 2, 1996 pp. 449-477 Deaths and exposures by individual calendar year and individual years of age for the U.K. male assured lives experience over the recent past are comprehensively modelled using generalised linear modelling techniques. Their principal objective is to develop a model which incorporates both the age variation in mortality and the underlying time trends to the mortality rates. The approach has considerable advantages over ad hoe methods of fitting parametric models to represent the age variation in mortality and then separately attempting to represent the time trends in the parameters of these models. The approach advocated can be seen as an extension to the conventional parametric graduation techniques used by the CMI Bureau to represent trends in mortality. Keywords: Mortality trends, Cohort mortality, Modelling.
o92oos (M10) An Actuarial Survey of Statistical Models for Decrement and Transition Data II" Competing Risks, Non-Parametric and Regression Models MacDonald A.S., British Actuarial Journal, Nr. 2,
1996, pp.429-448 This paper surveys some statistical models of survival data. Competing risks models are described, the unidentifiability of net decrements suggests a skeptical approach to the use of underlying single decrement
tables. Approaches based on observation of complete lifetimes (with censoring) are surveyed including the Kaplan-Meier and Nelson-Aalen estimates. Regression models for lifetimes depending on covadates are discussed. In particular the Cox model and partial likelihood estimation. Keywords: Competing risks, Cox model, Kaplan-Meier estimate, Nelson-Aalen estimate, Partial likelihood, Proportional hazards, Survival analysis. 092009 (M10) Bayesian Methods in Actuarial Science Makon U.E., Smith A.F.M., Liu Y.-H,
The Statistician, Nr. 45, 1996, pp. 503-515 Statistical methods with a Bayesian flavour, in particular credibility theory, have long been used in the insurance industry as part of the process of estimating risks and setting premiums. Typically however, fully Bayesian analysis has proved computationally infeasible and various approximate solutions have been proposed. The first part of this paper provides a survey of such problems and the kinds of solution suggested in the actuarial literature. The second part reviews recent advances in Bayesian computational methodology and illustrates how it opens the way to a fully Bayesian treatment of a range of actuarial problems. Keywords: Bayesian models, Credibility theory, Graduation, Markov chain Monte Carlo method. 092010 (M10) Generalized Linear Models and Actuarial Science Haberman S., Renshaw A.E., The Statistician, Nr. 45,
1996 The authors review the application of generalized linear models to actuarial problems. This risk class of statistical model has been successfully applied in recent years to a wide range of problems, involving mortality, multiple-state models, lapses, premium rating and reserving. Selective examples of these applications are presented. Keywords: Generalized linear models, Life-insurance and non-life-insurance models.
092011 (M10) A Primer on Quantile Estimation Embrechts P., Presented at the International Workshop
on The Interplay between Insurance, Finance and Control, organized by the Mathematical Research Centre at Aarhus University, also supported by the Danish Science Research Council and the Centre for
Abstractsand Reviews
Process Models MacDonald A.S., British Actuarial Journal, Nr. 2,
1996, 703-726 Counting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial eduction is discussed. Keywords: Censoring, Compensators, Counting processes, Kaplan-Meier estimate, Martingales, Multiple state models, Nelson-Aalen estimate, Partial likelihood, Survival Analysis. 092007 (M10) The Modelling of Recent Mortality Trends in United Kingdom Male Assured Lives Renshaw A.E., Haberman S., Hatzopoulos P., British
Actuarial Journal, Nr. 2, 1996 pp. 449-477 Deaths and exposures by individual calendar year and individual years of age for the U.K. male assured lives experience over the recent past are comprehensively modelled using generalised linear modelling techniques. Their principal objective is to develop a model which incorporates both the age variation in mortality and the underlying time trends to the mortality rates. The approach has considerable advantages over ad hoe methods of fitting parametric models to represent the age variation in mortality and then separately attempting to represent the time trends in the parameters of these models. The approach advocated can be seen as an extension to the conventional parametric graduation techniques used by the CMI Bureau to represent trends in mortality. Keywords: Mortality trends, Cohort mortality, Modelling.
o92oos (M10) An Actuarial Survey of Statistical Models for Decrement and Transition Data II" Competing Risks, Non-Parametric and Regression Models MacDonald A.S., British Actuarial Journal, Nr. 2,
1996, pp.429-448 This paper surveys some statistical models of survival data. Competing risks models are described, the unidentifiability of net decrements suggests a skeptical approach to the use of underlying single decrement
tables. Approaches based on observation of complete lifetimes (with censoring) are surveyed including the Kaplan-Meier and Nelson-Aalen estimates. Regression models for lifetimes depending on covadates are discussed. In particular the Cox model and partial likelihood estimation. Keywords: Competing risks, Cox model, Kaplan-Meier estimate, Nelson-Aalen estimate, Partial likelihood, Proportional hazards, Survival analysis. 092009 (M10) Bayesian Methods in Actuarial Science Makon U.E., Smith A.F.M., Liu Y.-H,
The Statistician, Nr. 45, 1996, pp. 503-515 Statistical methods with a Bayesian flavour, in particular credibility theory, have long been used in the insurance industry as part of the process of estimating risks and setting premiums. Typically however, fully Bayesian analysis has proved computationally infeasible and various approximate solutions have been proposed. The first part of this paper provides a survey of such problems and the kinds of solution suggested in the actuarial literature. The second part reviews recent advances in Bayesian computational methodology and illustrates how it opens the way to a fully Bayesian treatment of a range of actuarial problems. Keywords: Bayesian models, Credibility theory, Graduation, Markov chain Monte Carlo method. 092010 (M10) Generalized Linear Models and Actuarial Science Haberman S., Renshaw A.E., The Statistician, Nr. 45,
1996 The authors review the application of generalized linear models to actuarial problems. This risk class of statistical model has been successfully applied in recent years to a wide range of problems, involving mortality, multiple-state models, lapses, premium rating and reserving. Selective examples of these applications are presented. Keywords: Generalized linear models, Life-insurance and non-life-insurance models.
092011 (M10) A Primer on Quantile Estimation Embrechts P., Presented at the International Workshop
on The Interplay between Insurance, Finance and Control, organized by the Mathematical Research Centre at Aarhus University, also supported by the Danish Science Research Council and the Centre for