General tax structures for a Lévy insurance risk process under the Cramér condition

Research output: Contribution to journalArticle

Abstract

We investigate the Lévy insurance risk model with tax under Cramér's condition. A direct analogue of Cramér's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin occurring, of several variables of interest related to ruin including the surplus immediately prior to ruin (undershoot)and shortfall at ruin (overshoot). We also compute the present value of all tax paid conditional on ruin occurring. The proof involves first transferring results from the model with no tax to the reflected process, and from there to the model with tax.

Original languageEnglish (US)
JournalStochastic Processes and their Applications
DOIs
StatePublished - Jan 1 2019

Fingerprint

Risk Process
Insurance
Tax
Taxation
Direct analogs
Probability of Ruin
Overshoot
Several Variables
Model
Asymptotic distribution
Immediately
Analogue
Estimate

Keywords

  • Cramér condition
  • First passage time
  • Lévy insurance risk process
  • Overshoot
  • Reflected process
  • Tax structures

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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title = "General tax structures for a L{\'e}vy insurance risk process under the Cram{\'e}r condition",
abstract = "We investigate the L{\'e}vy insurance risk model with tax under Cram{\'e}r's condition. A direct analogue of Cram{\'e}r's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin occurring, of several variables of interest related to ruin including the surplus immediately prior to ruin (undershoot)and shortfall at ruin (overshoot). We also compute the present value of all tax paid conditional on ruin occurring. The proof involves first transferring results from the model with no tax to the reflected process, and from there to the model with tax.",
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AB - We investigate the Lévy insurance risk model with tax under Cramér's condition. A direct analogue of Cramér's estimate for the probability of ruin in this model is obtained, together with the asymptotic distribution, conditional on ruin occurring, of several variables of interest related to ruin including the surplus immediately prior to ruin (undershoot)and shortfall at ruin (overshoot). We also compute the present value of all tax paid conditional on ruin occurring. The proof involves first transferring results from the model with no tax to the reflected process, and from there to the model with tax.

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KW - Overshoot

KW - Reflected process

KW - Tax structures

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