## Abstract

The idea of taxation in risk process was first introduced by Albrecher, H. & Hipp, C. Lundberg’s risk process

with tax. Blätter der DGVFM 28(1), 13–28, who suggested that a certain proportion of the insurer’s income

is paid immediately as tax whenever the surplus process is at its running maximum. In this paper, a spectrally

negative Lévy insurance risk model under taxation is studied. Motivated by the concept of randomized

observations proposed by Albrecher, H., Cheung, E.C.K. & Thonhauser, S. Randomized observation periods

for the compound Poisson risk model: Dividends. ASTIN Bulletin 41(2), 645–672, we assume that the

insurer’s surplus level is only observed at a sequence of Poisson arrival times, at which the event of ruin

is checked and tax may be collected from the tax authority. In particular, if the observed (pre-tax) level

exceeds the maximum of the previously observed (post-tax) values, then a fraction of the excess will be

paid as tax. Analytic expressions for the Gerber–Shiu expected discounted penalty function and the expected

discounted tax payments until ruin are derived. The Cramér-Lundberg asymptotic formula is shown to hold

true for the Gerber–Shiu function, and it differs from the case without tax by a multiplicative constant. Delayed

start of tax payments will be discussed as well. We also take a look at the case where solvency is monitored

continuously (while tax is still paid at Poissonian time points), as many of the above results can be derived in

a similar manner. Some numerical examples will be given at the end.

with tax. Blätter der DGVFM 28(1), 13–28, who suggested that a certain proportion of the insurer’s income

is paid immediately as tax whenever the surplus process is at its running maximum. In this paper, a spectrally

negative Lévy insurance risk model under taxation is studied. Motivated by the concept of randomized

observations proposed by Albrecher, H., Cheung, E.C.K. & Thonhauser, S. Randomized observation periods

for the compound Poisson risk model: Dividends. ASTIN Bulletin 41(2), 645–672, we assume that the

insurer’s surplus level is only observed at a sequence of Poisson arrival times, at which the event of ruin

is checked and tax may be collected from the tax authority. In particular, if the observed (pre-tax) level

exceeds the maximum of the previously observed (post-tax) values, then a fraction of the excess will be

paid as tax. Analytic expressions for the Gerber–Shiu expected discounted penalty function and the expected

discounted tax payments until ruin are derived. The Cramér-Lundberg asymptotic formula is shown to hold

true for the Gerber–Shiu function, and it differs from the case without tax by a multiplicative constant. Delayed

start of tax payments will be discussed as well. We also take a look at the case where solvency is monitored

continuously (while tax is still paid at Poissonian time points), as many of the above results can be derived in

a similar manner. Some numerical examples will be given at the end.

Original language | English |
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Pages (from-to) | 51-87 |

Journal | Scandinavian Actuarial Journal |

Volume | 2017 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |