带扩散扰动的对偶风险模型的门槛分红策略

摘要

研究了一类带干扰(布朗运动)的对偶风险模型,此模型可以用来模拟证券公司的盈余过程(经营收入).利用无穷小分析法,求出了公司在破产前总分红现值期望函数(分红函数)满足的微积分方程组,导出了与该微积分方程组等价的更新方程组.最后,在指数分布收入情形下,我们给出了分红函数在特例下的一般解.%The dual risk model perturbed by diffusion (Brownian motion) was studied. The surplus process (operating income) of a securities company could be simulated by this model. Using the infinitesimal analysis, the integro differential equations of the expected accumulated discounted dividends before bankruptcy were obtained. Then, the renewal equations equivalent to the integro-differential equations were derived. Finally, for exponentially distributed income, the explicit solutions for the expected accumulated discounted dividends were given for special cases.