Applied Stochastic Models in Business and Industry

Yang, Zhenlin; Lin, Dennis K. J.

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.678

The biasness problem of the maximum‐likelihood estimate (MLE) of the common shape parameter of several Weibull populations is examined in detail. A modified MLE (MMLE) approach is proposed. In the case of complete and Type II censored data, the bias of the MLE can be substantial. This is noticeable even when the sample size is large. Such a bias increases rapidly as the degree of censorship increases and as more populations are involved. The proposed MMLE, however, is nearly unbiased and much more efficient than the MLE, irrespective of the degree of censorship, the sample sizes, and the number of populations involved. Copyright © 2007 John Wiley & Sons, Ltd.

Delwarde, Antoine; Denuit, Michel; Partrat, Christian

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.679

Mortality improvements pose a challenge for the planning of public retirement systems as well as for the private life annuities business. For public policy, as well as for the management of financial institutions, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp(αx + βxκt). The log of the time series of age‐specific death rates is thus expressed as the sum of an age‐specific component αx that is independent of time and another component that is the product of a time‐varying parameter κt reflecting the general level of mortality, and an age‐specific component βx that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. The parameters are usually estimated via singular value decomposition or via maximum likelihood in a binomial or Poisson regression model. This paper demonstrates that it is possible to take into account the overdispersion present in the mortality data by estimating the parameter in a negative binomial regression model. Copyright © 2007 John Wiley & Sons, Ltd.

Frangos, N. E.; Vrontos, S. D.; Yannacopoulos, A. N.

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.680

We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long‐range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd.

Wang, Xikui; Pai, Jeffrey S.; Shand, Kevin J.

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.681

We use a semi‐Markov model to analyse the stochastic dynamics of disease occurrence of dogs insured in Canada from 1990 to 1999, and the probability pattern of death from illness. After statistically justifying the use of a stochastic model, we demonstrate that a stationary first‐order semi‐Markov process is appropriate for analysing the available data set. The probability transition function is estimated and its stationarity is tested statistically. Homogeneity of the semi‐Markov model with respect to important covariates (such as geographic location, insurance plan, breed and age) is also statistically examined. We conclude with discussions and implications of our results in veterinary contents. Copyright © 2007 John Wiley & Sons, Ltd.

Caporale, Guglielmo Maria; Gil‐Alana, Luis A.

2007 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.683

In a recent paper, Yoon (Working Paper, Department of Economics and Related Studies, University of York, 2003. Presented at the ESF‐EMM Second Annual Meeting, Rome, Italy, 2003) asserts that the stochastic unit root (STUR) model is closely related to long memory processes, and, in particular, that it is a special case of an I(d) process, with d = 1.5. In this paper we question this claim by using parametric and semiparametric techniques for modelling long memory. We extend the analysis by considering both non‐normality and seasonality, and shed light, theoretically and by means of Monte Carlo methods, on the relationship between the seasonal STUR and the seasonal I(d) models. The results show that methods that are specifically designed for testing I(d) statistical models are not appropriate for testing the STUR model. Moreover, they have in some cases very low power against STUR alternatives. Copyright © 2007 John Wiley & Sons, Ltd.