In this paper, a jump-diffusion Omega model with a two-step premium rate and a threshold dividend strategy is studied. For this model, the surplus process is a perturbation of a compound Poisson process by a Brownian motion. Firstly, using the strong Markov property, the integro-differential equations for the expected discounted dividend payments function, the Gerber-Shiu expected discounted penalty function and bankruptcy probability are derived. Secondly, for a constant bankruptcy rate function, the renewal equations satisfied by the expected discounted dividend payments function and the Gerber-Shiu expected discounted penalty function are obtained, respectively, and by iteration, their closed-form solutions are also given. Furthermore, the explicit solutions of the two kinds of functions are obtained when the individual claim size is subject to exponential distribution. Finally, a numerical example is presented to illustrate some properties of the Omega model.

本文研究了具有两步溢价率和阈值分红策略的跳扩散Omega模型。对于此模型，剩余过程是布朗运动对复合泊松过程的扰动。首先，利用强大的马尔可夫性质，推导了预期的折现股利支付函数的积分微分方程，Gerber-Shiu的预期折现罚金函数和破产概率。其次，对于一个恒定的破产率函数，分别得到了期望折现股利支付函数和Gerber-Shiu期望折现罚金函数所满足的更新方程，并通过迭代给出了它们的闭式解。此外，当个体索赔的大小服从指数分布时，就可以得到两种函数的显式解。最后，给出一个数值示例来说明Omega模型的一些属性。