Title: The equivalence of two tax processes,
Abstract: We introduce two models of taxation, the latent and natural tax processes,
which have both been used to represent loss-carry-forward taxation on the
capital of an insurance company. In the natural tax process, the tax rate is a
function of the current level of capital, whereas in the latent tax process,
the tax rate is a function of the capital that would have resulted if no tax
had been paid. Whereas up to now these two types of tax processes have been
treated separately, we show that, in fact, they are essentially equivalent.
This allows a unified treatment, translating results from one model to the
other. Significantly, we solve the question of existence and uniqueness for the
natural tax process, which is defined via an integral equation. Our results
clarify the existing literature on processes with tax.