Yang Chen, Kristina P. Sendova, Zhong Li

Publication:

Insurance: Mathematics and Economics

Abstract:

We consider the threshold dividend strategy where a company’s surplus process is described by thedual Lévyrisk model. Namely, the company chooses to pay dividends at a constant rate only whenthe surplus is above some nonnegative threshold. Classically, such a company is referred to be ruinedimmediately when the surplus level becomes negative. Recently, researchers investigate the Parisianruin problem where the company is allowed to operate under negative surplus for a predeterminedperiod known as the Parisian delay. With the help of the fluctuation identities of spectrally negativeLévyprocesses, we obtain an explicit expression of the expected discounted dividends until Parisianruin in terms of the relevant scale functions and certain probabilities that need to be evaluated for eachspecific Lévyprocess. The optimal threshold level under such a threshold dividend strategy is deduced.Applications and numerical examples are given to illustrate the theoretical results and examine howthe expected discounted aggregate dividends and the optimal threshold level change in response todifferent Parisian delays.