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On a constant interest risk model with debit interest and tax payments. (English) Zbl 1313.91084

Summary: A constant interest risk model with debit interest and tax payments according to a loss-carried-forward system is investigated. Whenever the surplus is in a portfolio situation, the insurer may pay a certain proportion of the premium and the interest income as tax payments. Whenever the surplus is nonnegative, the insurer will earn interest with force \(r>0\). Whenever the surplus is below zero, the insurer could borrow money at a debit interest rate \(\delta>0\) to pay claims. An explicit expression for the expected discounted tax payments until absolute ruin is derived.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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