ИСТИНА

We study the life annuity (or pension) insurance model with random revenues when the whole surplus of the insurer is invested continuously in a risk-free asset. For the survival probability as a function of the initial surplus in this model, some associated singular problem for linear integro-differential equation (IDE) was formulated and studied earlier. Here we provide the sufficiency theorem asserting that the solution of associated singular problem for IDE determines the survival probability in the original insurance model.