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

Philip S. Griffin

doi:10.1016/j.spa.2019.05.003

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

Philip S. Griffin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	1368-1387
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	3
DOIs	https://doi.org/10.1016/j.spa.2019.05.003
State	Published - Mar 2020

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

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10.1016/j.spa.2019.05.003

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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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N2 - 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.

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.

KW - Cramér condition

KW - First passage time

KW - Lévy insurance risk process

KW - Overshoot

KW - Reflected process

KW - Tax structures

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

Abstract

Keywords

ASJC Scopus subject areas

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