A Journal "Theory of Probability and Mathematical Statistics"
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# Theory of Probability and Mathematical Statistics

## DIVIDENDS WITH TAX AND CAPITAL INJECTION IN A SPECTRALLY NEGATIVE LEVY RISK MODEL

### H. SCHMIDLI

Abstract: We consider a risk model driven by a spectrally negative L'evy process. From the surplus dividends are paid and capital injections have to be made in order to keep the surplus positive. In addition, tax has to be paid for dividends, but injections lead to an exemption from tax. We generalize the results from [12, 13] and show that the optimal dividend strategy is a two-barrier strategy. The barrier depends on whether an immediate dividend would be taxed or not. For a risk process perturbed by di usion with exponentially distributed claim sizes, we show how the value function and the barriers can be determined.

Keywords: L'evy risk model, dividends, capital injections, tax, barrier strategy, Hamilton-Jacobi-Bellman equation, perturbed risk model.

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