On the closed-form expected NPVs of the double barrier strategy for regular diffusions under the bail-out setting

Abstract

The core of the research is to provide the explicit expression for the expected net present values (NPVs) of the double barrier strategy for regular diffusions. Under the so-called bail-out setting, the value of the expected NPVs of an insurance company varies according to the choice of a pair of policies, which consist of dividend payments paid out and capital injections received. In the case of the double barrier strategy, the closed-form expected NPVs are given via the bivariate q-scale function. This is accomplished by making use of a perturbation technique in [CP14], which could lead to the linear equation system. The expression obtained here shall be conducive to addressing the associated dividends control problems.