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On the classical risk model with credit and debit interests under absolute ruin. (English) Zbl 1183.91078

Summary: We consider the dividend payments in a compound Poisson risk model with credit and debit interests under absolute ruin. We first obtain the integro-differential equations satisfied by the moment generating function and moments of the discounted aggregate dividend payments. Secondly, applying these results, we get the explicit expressions of them for exponential claims. Then, we give the numerical analysis of the optimal dividend barrier and the expected discounted aggregate dividend payments which are influenced by the debit and credit interests. Finally, we find the integro-differential equations satisfied by the Laplace transform of absolute ruin time and give its explicit expressions when the claim sizes are exponentially distributed.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G30 Interest rates, asset pricing, etc. (stochastic models)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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