On the joint distribution of tax payments and capital injections for a Lévy risk model
Słowa kluczowe:Two-sided reflection, finite buffer, dividends, net present value, scale functions
ON THE JOINT DISTRIBUTION OF TAX PAYMENTS AND CAPITAL INJECTIONS FOR A LÉVY RISK MODEL
We study the joint distribution of tax payments according toa loss-carry-forward scheme and capital injections in a Lévy risk model, andprovide a transparent expression for the corresponding transform in terms ofthe scale function. This allows us to identify the net present value of capitalinjections in such a model, complementing the one for tax found in ourpaper . 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 netpresent value of taxes and injections is given.