Band 39, Heft 1-2

One of the important issues is risk assessment and calculation in complex and multi-component systems. In this paper, the estimation of multi-component stress-strength reliability for the Weibull distribution under the progressive Type-II censored samples is studied. We assume that both stress and strength are two independent Weibull distributions with different parameters. First, assuming the same shape parameter, the maximum likelihood estimation (MLE), different approximations of Bayes estimators (Lindley’s approximation and Markov chain Monte Carlo method) and different confidence intervals (asymptotic and highest posterior density) are obtained. In the case when the shape parameter is known, the MLE, uniformly minimum variance unbiased estimator (UMVUE), exact Bayes estimator and different confidence intervals (asymptotic and highest posterior density) are considered. Finally, in the general case, the statistical inferences on multi-component stress-strength reliability are derived. To compare the performances of different methods, Monte Carlo simulations are performed. Moreover, one data set for illustrative purposes is analyzed.

Major events like the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined, it is important to consider models which reflect this dependence. In this paper, we make a proposal on how to generate dependence between the financial market and claim sizes in times of crisis and determine via a stochastic control approach an optimal investment and reinsurance strategy which maximizes the expected exponential utility of terminal wealth. Moreover, we also allow that the claim size distribution may be learned in the model. We give comparisons and bounds on the optimal strategy using simple models. What turns out to be very surprising is that numerical results indicate that even a minimal dependence which is created in this model has a huge impact on the optimal investment strategy.