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Optimal dividend strategies for a risk process under force of interest


  • Albrecher, Hansjörg
  • Thonhauser, Stefan


In the classical Cramér-Lundberg model in risk theory the problem of maximizing the expected cumulated discounted dividend payments until ruin is a widely discussed topic. In the most general case within that framework it is proved [Gerber, H.U., 1968. Entscheidungskriterien fuer den zusammengesetzten Poisson-prozess. Schweiz. Aktuarver. Mitt. 1, 185-227; Azcue, P., Muler, N., 2005. Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model. Math. Finance 15 (2) 261-308; Schmidli, H., 2008. Stochastic Control in Insurance. Springer] that the optimal dividend strategy is of band type. In the present paper we discuss this maximization problem in a generalized setting including a constant force of interest in the risk model. The value function is identified in the set of viscosity solutions of the associated Hamilton-Jacobi-Bellman equation and the optimal dividend strategy in this risk model with interest is derived, which in the general case is again of band type and for exponential claim sizes collapses to a barrier strategy. Finally, an example is constructed for Erlang(2)-claim sizes, in which the bands for the optimal strategy are explicitly calculated.

Suggested Citation

  • Albrecher, Hansjörg & Thonhauser, Stefan, 2008. "Optimal dividend strategies for a risk process under force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 134-149, August.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:134-149

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    References listed on IDEAS

    1. Albrecher, Hansjorg & Teugels, Jozef L. & Tichy, Robert F., 2001. "On a gamma series expansion for the time-dependent probability of collective ruin," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 345-355, December.
    2. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach," Finance and Stochastics, Springer, vol. 5(3), pages 275-303.
    3. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    4. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
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    Cited by:

    1. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    2. F. Avram & Z. Palmowski & M. R. Pistorius, 2011. "On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function," Papers 1110.4965,, revised Jun 2015.
    3. repec:gam:jrisks:v:6:y:2018:i:1:p:1-:d:125805 is not listed on IDEAS
    4. Irmina Czarna & Zbigniew Palmowski, 2010. "Dividend problem with Parisian delay for a spectrally negative L\'evy risk process," Papers 1004.3310,, revised Oct 2011.
    5. repec:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0283-y is not listed on IDEAS
    6. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747,, revised Feb 2014.
    7. repec:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9726-x is not listed on IDEAS
    8. Martin Hunting & Jostein Paulsen, 2013. "Optimal dividend policies with transaction costs for a class of jump-diffusion processes," Finance and Stochastics, Springer, vol. 17(1), pages 73-106, January.
    9. Zhu, Jinxia & Chen, Feng, 2015. "Dividend optimization under reserve constraints for the Cramér–Lundberg model compounded by force of interest," Economic Modelling, Elsevier, vol. 46(C), pages 142-156.
    10. Yu, Wenguang, 2013. "Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests," Economic Modelling, Elsevier, vol. 31(C), pages 625-634.

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