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Optimal loss-carry-forward taxation for the Lévy risk model. (English) Zbl 1238.91086

This paper investigates an optimal loss-carry-forward taxation problem when the reserve process of an insurance company is governed by a spectrally negative Lévy process. The objective is to find the optimal tax return function and the optimal tax policy that maximize the expected accumulated discounted tax payout until the time of ruin of the insurance company. Two situations are classified and analysed. In the first situation, the optimal strategy is to always pay tax at the maximum rate. Whereas, in the second situation, the optimal strategy is to pay tax at the smallest rate when the reserve is below some critical level and to pay at the maximum rate when the reserve is above the critical level.

MSC:

91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
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