Bayesian Methods in Actuarial Science

Abstract

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 solutions 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.

Fuzzy formulation of the Lee–Carter model for mortality forecasting

“…The key principle in Bayesian analysis is that the posterior distribution of a parameter, conditioned on the data, is proportional to the product of its likelihood function and its prior distribution (Gelman et al, 1995, p. 8). Bayesian analysis was intensively studied and its applications cover areas such as econometrics (Gelman et al, 1995), physics (D'Agostini, 2003), health and social sciences (Congdon, 2003), actuarial sciences (Scollnik, 2001;Pai, 1997;Makov et al, 1996;Shapiro, 1979).…”

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

“…Reviews of the MCMC method, BUGS, and their application in actuarial science can be found in Scollnik (2001). See Makov et al (1996) for a more general discussion of Bayesian methods in actuarial science.…”

Posterior Regret Γ-Minimax Estimation of Insurance Premium in Collective Risk Model

“…The square-error loss function has been considered in many papers about Bayesian analysis in the risk theory, see Makov et al (1996), Klugman (1992), Klugman et al (1998) for examples. Being symmetric, the square-error loss equally penalizes over-and under-estimation of the same magnitude.…”