Stochastic comparison of generalized combined risk processes

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Usually, two different types of shock models (extreme and cumulative shock models) are employed to model the dynamic risk processes. In extreme shock models, only the impact of the current fatal shock is usually taken into account, whereas, in cumulative shock models, the impact of the preceding shocks is accumulated as well. However, in practice, the effect of the corresponding shock can be realized in those two ways in one model (i.e., it can be fatal or, otherwise it is accumulated). This observation justifies the consideration of a 'combined shock model' in the risk modeling and analysis. In this paper, we generalize the study of the dynamic risk processes that were previously considered in the literature. The main theme of this paper is to find the optimal allocation policies for the generalized combined risk processes via the stochastic comparisons of survival functions. It will be seen that the obtained results hold for 'general counting processes' of shocks. In addition, we consider the problem of maximizing a gain function under certain risks and obtain reasonable decisions based on a variability measure. Furthermore, the meaningful explanations for the results on the policy ordering will be provided.

Original languageEnglish
Pages (from-to)818-826
Number of pages9
JournalJournal of Statistical Planning and Inference
Issue number4
StatePublished - Apr 2013

Bibliographical note

Funding Information:
The author greatly thanks the referee for a careful reading of the paper and helpful suggestions, which have improved the presentation of the paper. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2011-0017338 ). The author would like to appreciate Mrs. Sul Ja Choi for helpful discussions on the practical aspects of the models considered in this paper.


  • Combined shock model
  • Optimal transportation
  • Policy ordering
  • Stability
  • Stochastic order


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