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

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.

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.

Keywords

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

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

Cite this paper

nullJ. Tan, L. Xiao, S. Liu and X. Yang, "Moments of Discounted Dividend Payments in the Sparre Andersen Model with a Constant Dividend Barrier,"*Applied Mathematics*, Vol. 2 No. 4, 2011, pp. 444-451. doi: 10.4236/am.2011.24056.

nullJ. Tan, L. Xiao, S. Liu and X. Yang, "Moments of Discounted Dividend Payments in the Sparre Andersen Model with a Constant Dividend Barrier,"

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