Fluctuation theory for level-dependent Lévy risk processes

  title={Fluctuation theory for level-dependent L{\'e}vy risk processes},
  author={Irmina Czarna and Jos'e Luis P'erez and Tomasz Rolski and Kazutoshi Yamazaki},
  journal={Stochastic Processes and their Applications},

A Review of First-Passage Theory for the Segerdahl-Tichy Risk Process and Open Problems

Four methods for computing the basic functions of spectrally negative Levy and diffusion processes, based on identifying two “basic” monotone harmonic functions/martingales have been developed are reviewed, with the purpose of drawing attention to connections between them, to underline open problems, and to stimulate further work.

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The Segerdahl process (Segerdahl (1955)), characterized by exponential claims and affine drift, has drawn a considerable amount of interest—see, for example, (Tichy (1984); Avram and Usabel (2008);

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