Within this paper we consider a barrier problem in the collective risk theory model, under the presence of a constant interest intensity to which the reserve is invested. Referring to such model, after the consideration of the traditional linear barrier, we suggest barriers depending on the above intensity. We obtain some equations fulfilled by the ruin probability and the dividends present value and some conditions. Our study invests both on the case where the ruin occurs when the barrier becomes negative and on the case where the ruin falls down an appropriate negative level, depending on premium flow and the barrier.
Reserves and barriers under interest force in a risk process
GOSIO, CRISTINA;LARI, ESTER CESARINA;RAVERA, MARINA
2010-01-01
Abstract
Within this paper we consider a barrier problem in the collective risk theory model, under the presence of a constant interest intensity to which the reserve is invested. Referring to such model, after the consideration of the traditional linear barrier, we suggest barriers depending on the above intensity. We obtain some equations fulfilled by the ruin probability and the dividends present value and some conditions. Our study invests both on the case where the ruin occurs when the barrier becomes negative and on the case where the ruin falls down an appropriate negative level, depending on premium flow and the barrier.
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