In the framework of collective risk theory models, the dynamic solvency insurance contract is studied. Whenever the reserve falls below the ruin level, such a contract provides a payment in the amount of the deficit. The paper focuses on the net single premium of solvency insurance by considering two different definitions of ruin, referring to models modified by the inclusion of an upper reflecting barrier. The main results are integral and integro-differential equations for the net single premium. An exact solution is given in the special case with exponential claim sizes and zero interest force.

This paper refers to the collective risk theory model modified by the inclusion of interest at a constant force .

According to Gerber (1974 and 1981) and Vittal and Vasudevan (1987), we consider a model modified by the presence of an upper reflecting barrier. We assume that when the reserve reaches the above barrier, the difference between the reserve itself and the barrier is paid out as a ‘dividend payment’ until the occurrence of the next claim.

We consider the dynamic solvency insurance contract proposed by Gerber and Pafumi (1998); such a contract, in the event that the reserve falls below the ruin level, provides a payment in the amount of the deficit so that the reserve is immediately reset to the minimum value necessary to avoid the ruin. The authors studied the case where the reserve is controlled by a Wiener process, highlighting the benefits resulting from such a model. They also emphasized that the Wiener process is less realistic than the compound Poisson model.

We assume the compound Poisson model and derive the integral and integro-differential equations for the net single premium (Pafumi, 1998) (discussion of Gerber and Shiu, 1998), and subsequently, Dickson and Waters (2004) give some results when d = 0.

The ruin of an insurance company is defined as follows: “Ruin occurs once its reserve becomes negative or once its reserve falls below a negative level” (Gerber, 1971). We consider the classical level zero and a new appropriate negative level.

The paper first presents the collective risk theory modified model, introduces the dynamic solvency insurance contract and studies the net single premium of such contract. The paper then derives the integro-differential equations for net single premiums, followed by an example.

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