H. U. Gerber, E. S. W. Shiu and N. Smith, “Methods for Estimating the Optimal Dividend Barrier and the Probability of Ruin,” Insurance: Mathematics and Economics, Vol. 42, No. 2, 2008, pp. 243-254. doi:10.1016/j.insmatheco.2007.02.002

has been cited by the following article:

• TITLE: Moments of Discounted Dividend Payments in the Sparre Andersen Model with a Constant Dividend Barrier

  AUTHORS: Jiyang Tan, Lin Xiao, Shaoyue Liu, Xiangqun Yang

  KEYWORDS: Sparre Andersen Model, Expected Discounted Penalty Function, Constant Dividend Barrier, Recursion, Iteration

  JOURNAL NAME: Applied Mathematics, Vol.2 No.4, March 31, 2011

  ABSTRACT: We consider the Sparre Andersen risk process in the presence of a constant dividend barrier, and propose a new expected discounted penalty function which is different from that of Gerber and Shiu. We find that iteration mothed can be used to compute the values of expected discounted dividends until ruin and the new penalty function. Applying the new function and the recursion method proposed in Section 5, we obtain the arbitrary moments of discounted dividend payments until ruin.