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On a Dual Model with Barrier Strategy

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  • Yuzhen Wen
  • Chuancun Yin

Abstract

We consider the dual of the generalized Erlang(n) risk model with a barrier dividend strategy. We derive integro‐differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment‐generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples.

Suggested Citation

  • Yuzhen Wen & Chuancun Yin, 2012. "On a Dual Model with Barrier Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:343794
    DOI: 10.1155/2012/343794
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    References listed on IDEAS

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    1. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    2. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    3. Avanzi, Benjamin & Gerber, Hans U., 2008. "Optimal Dividends in the Dual Model with Diffusion," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 653-667, November.
    4. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
    5. Chi, Yichun & Lin, X. Sheldon, 2011. "On the threshold dividend strategy for a generalized jump-diffusion risk model," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 326-337, May.
    6. Cheung, Eric C.K. & Drekic, Steve, 2008. "Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 399-422, November.
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