In the collective risk theory framework we consider a model in which the reserve earns interest at a constant rate . In this model we consider the dynamic solvency insurance contract (proposed by Gerber and Pafumi, 1998) and the dividends paid according to a linear dividend barrier. We assume that the ruin occurs whenever the reserve falls below a suitable level k and we analyze the possible values of k. We derive a general equation for dividends expected present value. We also give an integro-differential equation with boundary conditions. Finally, we present some cases of interest and a particular case where an explicit solution can be obtained.
Dividends and Dynamic Solvency Insurance
GOSIO, CRISTINA;LARI, ESTER CESARINA;RAVERA, MARINA
2011-01-01
Abstract
In the collective risk theory framework we consider a model in which the reserve earns interest at a constant rate . In this model we consider the dynamic solvency insurance contract (proposed by Gerber and Pafumi, 1998) and the dividends paid according to a linear dividend barrier. We assume that the ruin occurs whenever the reserve falls below a suitable level k and we analyze the possible values of k. We derive a general equation for dividends expected present value. We also give an integro-differential equation with boundary conditions. Finally, we present some cases of interest and a particular case where an explicit solution can be obtained.
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