ON THE JOINT DISTRIBUTION OF TAX PAYMENTS AND CAPITAL
INJECTIONS FOR A LÉVY RISK MODEL
Hansjörg Albrecher
Jevgenijs Ivanovs
Abstract: We study the joint distribution of tax payments according to a loss-carry-forward
scheme and capital injections in a Lévy risk model, and provide a transparent expression for
the corresponding transform in terms of the scale function. This allows us to identify the net
present value of capital injections in such a model, complementing the one for tax found in
our paper [3]. We also apply the result to the situation when injections may be stopped at a
constant rate, and in this case an explicit formula for the net present value of taxes and
injections is given.
2010 AMS Mathematics Subject Classification: Primary: 60G51; Secondary:
60E10.
Keywords and phrases: Two-sided reflection, finite buffer, dividends, net present value,
scale functions.