Suchergebnisse

In considering life insurance contracts, durational effects may appear at two levels. The first is concerned with the underlying biometrical risk, meaning that dependencies of transition probabilities on the previous duration in a certain state can be observed. Secondly, there is a need for duration-depending actuarial payments. The model presented here, based on semi-Markov processes, allows one to directly model dependencies on the previous duration. Relying on real data, numerical examples dealing with disability insurance as well as German private health insurance outline the impact of using duration-depending transition rates.

AbstractThis paper presents a new and flexible prognostics framework based on a higher‐order hidden semi‐Markov model (HOHSMM) for systems or components with unobservable health states and complex transition dynamics. The HOHSMM extends the basic hidden Markov model (HMM) by allowing the hidden state to depend on its more distant history and assuming generally distributed state duration. An effective Gibbs sampling algorithm is designed for statistical inference of the HOHSMM. We conduct a simulation study to evaluate the performance of the proposed HOHSMM sampler and examine the impacts of the distant‐history dependency. We design a decoding algorithm to estimate the hidden health states using the learned model. Remaining useful life is predicted using a simulation approach given the decoded hidden states. The practical utility of the proposed prognostics framework is demonstrated by a case study on National Aeronautics and Space Administration (NASA) turbofan engines. We further compare the RUL prediction performance between the proposed HOHSMM and a benchmark mixture of Gaussians HMM prognostics method. The results show that the HOHSMM‐based prognostics framework provides good hidden health‐state assessment and RUL estimation for complex systems.

ABSTRACTThis paper reports an exploratory study of the development, application, and evaluation of a semi‐Markov model which forecasts personnel mobility rates within a major employer. The accuracy of the model is investigated by comparing the results generated by it to the results from a simple Markov model and to the observed behavior within the organization.

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers.