Abstract
In this contribution, the nonlinear dynamics of the surplus (net assets or reserve) process for a dividend-distributing company is studied in conjunction with the dynamics of its dividend equalization fund. The latter type of fund is maintained by leading insurance companies throughout the world and pays a special dividend for income that the investors lost because the dividend payment process was adversely affected for some or other reason. In our paper, a stochastic model for the related notion of a dividend equalization solvency ratio is derived. The ambient value of this ratio is an indication of the capacity of the insurer to pay dividends to shareholders especially when profit is low. The aforementioned analysis is, in turn, based on the construction of continuous time stochastic models for the dynamics of the surplus and total liabilities processes of an insurer. The discussions are reliant on principles arising within the asset-liability modelling paradigm.
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