Improvement to the Expected Discounted Penalty Function for a Classical Risk Model with a Threshold Dividend Strategy

Abstract:

In this paper, we study the expected discounted penalty function for a classical risk model in which a threshold dividend strategy is used for a classical risk model and the discount interest force process is not a constant, but a stochastic process driven by Poisson process and Wiener process. In this model, we derive and solve an integro-differential equation for the expected discounted penalty function.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 1150-1155
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.1150
• Online since: August 2010
• Authors: Wen Guang Yu, Zhi Liu
• Keywords: Expected Discounted Penalty Function, Integro-Differential Equation, Stochastic Interest, Threshold Dividend Strategy

References

[1] B. De Finetti, Su un' impostazione alternativa della teoria collectiva del rischio, Transactions of the XVth International Congress of Actuaries, Vol 2, 1957, pp.433-43.

[2] H.U. Gerber, E. Shiu, On optimal dividend strategies in the compound Poisson model, North American Actuarial Journal, Vol 10, 2006, pp.76-93.

DOI: 10.1080/10920277.2006.10596249

[3] X.S. Lin, G.E. Willmot, S. Drekic, The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function, Insurance: Mathematics and Economics, Vol 33, 2003, pp.551-566.

DOI: 10.1016/j.insmatheco.2003.08.004

[4] X.S. Lin, K.P. Pavlova, The compound Poisson risk model with a threshold dividend strategy, Insurance: Mathematics and Economics, Vol 38, 2006, pp.57-80.

DOI: 10.1016/j.insmatheco.2005.08.001

[5] H. Albrecher, J. Hatinger, A risk model with multilayer dividend strategy, North American Actuarial Journal, Vol 11, 2007, pp.43-64.

DOI: 10.1080/10920277.2007.10597447

[6] K.C. Yuen, G.J. Wang, W.K. Li, The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier, Insurance: Mathematics and Economics, Vol 40, 2007, pp.104-112.

DOI: 10.1016/j.insmatheco.2006.03.002

[7] X.W. Zhou, Classical risk model with multi-layer premium rate, Actuarial Research Clearing House 2007. 1. http: /soa. org/newsandpublications/publications/proceedings/arch.

[8] H.U. Gerber, E. Shiu, On optimal dividend strategy in the compound Poisson model, North American Actuarial Journal, Vol 10, 2005, pp.76-93.

DOI: 10.1080/10920277.2006.10596249

[9] P. Gary, A portfolio if endowment policies and its limiting distribution, Astin Bulletin, Vol 26, 1996, pp.25-33.

DOI: 10.2143/ast.26.1.563231

[10] J.A. Beekman, C.P. Fueling, One Approach to Dual Randomness in Life Insurance, Scand Actuar J., Vol 2, 1993, pp.173-182.

[11] W.J. He, Q.R. Jiang, Increasing life insurance under stochastic interes, Applied Mathematics of Chinese University, Vol 12A, 1998, pp.145-152.

[12] L. Liu, R. Wang, A class of increasing life insurance under stochastic interest, Chinese Journal of Applied Probability and Statistics, Vol 17, 2001, pp.283-290.

[13] H.U. Gerber, E. Shiu, On the time value of ruin, North American Actuarial Journal, Vol 2, 1998, pp.48-78.