1 - 5 of 5 Chapters
[“Ruin” is an event that an insurance company should avoid as much as possible. Ruin theory uses some methodologies to evaluate ruin-related quantities by modeling insurance surplus. In this introduction, we briefly discuss the classical ruin theory as initiated by Dr. F. Lundberg  and Dr. H....
[Lévy processes is a rich class of stochastic processes that includes Wiener processes and compound Poisson processes. It is a useful tool for modeling an insurance surplus because it has a small dispersion term and large shocks that represent insurance claims. In this chapter, we briefly...
[Historically, ruin theory has been mainly studied from a probabilistic point of view; the statistical aspect has not been focused on so much. However, if we apply the theory to practice, we always need the statistical inference in the final stage. In the recent years, there have been studies...
[In this chapter, we shall concentrate on statistical inference for ruin probability, which is an important final step in using the ruin probability in practice. As was seen in Sect. 1.1 or Sect. 2.3, since the ruin probability does not have a closed expression except for a few simple claim...
[In this final chapter, we discuss inference for the Gerber-Shiu function under the Lévy insurance risk models. Although we have discussed a parametric inference for a claim process, we shall discuss a semi-parametric inference in this chapter. In Sect. 4.3, we considered discrete samples of the...
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