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The equivalence of two tax processes. (English) Zbl 1431.91242

Summary: 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.

MSC:

91B64 Macroeconomic theory (monetary models, models of taxation)
60G51 Processes with independent increments; Lévy processes
93E20 Optimal stochastic control
91G05 Actuarial mathematics
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