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October 2018, 14(4): 1545-1564. doi: 10.3934/jimo.2018020

Analysis of a dynamic premium strategy: From theoretical and marketing perspectives

1. 

Department of Mathematics and Statistics, Hang Seng Management College, Hang Shin Link, Siu Lek Yuen, Shatin, N.T., Hong Kong, China

2. 

China Institute for Actuarial Science, Central University of Finance and Economics, China

* Corresponding author: Fangda Liu

Received  February 2017 Revised  June 2017 Published  January 2018

Premium rate for an insurance policy is often reviewed and updated periodically according to past claim experience in real-life. In this paper, a dynamic premium strategy that depends on the past claim experience is proposed under the discrete-time risk model. The Gerber-Shiu function is analyzed under this model. The marketing implications of the dynamic premium strategy will also be discussed.

Citation: Wing Yan Lee, Fangda Liu. Analysis of a dynamic premium strategy: From theoretical and marketing perspectives. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1545-1564. doi: 10.3934/jimo.2018020
References:
[1]

L. B. AfonsoA. D. Egidio dos Reis and H. R. Waters, Calculating continuous time ruin probabilities for a large portfolio with varying premium, ASTIN Bulletin, 39 (2009), 117-136. doi: 10.2143/AST.39.1.2038059.

[2]

L. B. AfonsoA. D. Egidio dos Reis and H. R. Waters, Numerical evaluation of continuous time ruin probabilities for a portfolio with credibility updated premiums, ASTIN Bulletin, 40 (2010), 399-414. doi: 10.2143/AST.40.1.2049236.

[3]

L. B. Afonso, Evaluation of ruin probabilities for surplus process with credibility and surplus dependent premium, Ph. D. Thesis, 2008.

[4]

S. Asmussen, On the ruin problem for some adapted premium rules, MaPhySto Research Report No. 5 University of Aarhus, Denmark., 1999.

[5] S. Asmussen and H. Albrecher, Ruin Probabilities, World Scientific, 2010.
[6]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, Gerber-Shiu analysis with a generalized penalty function, Scandinavian Actuarial Journal, 2010 (2010), 185-199.

[7]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, Structural properties of Gerber-Shiu function in dependent Sparre Andersen models, Insurance: Mathematics and Economics, 46 (2010), 117-126. doi: 10.1016/j.insmatheco.2009.05.009.

[8]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, On orderings and bounds in a generalized sparre andersen risk model, Applied Stochastic Models in Business and Industry, 27 (2011), 51-60. doi: 10.1002/asmb.837.

[9]

H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal, 2 (1998), 48-78. doi: 10.1080/10920277.1998.10595671.

[10]

D. LandriaultC. Lemieux and G. E. Willmot, An adaptive premium policy with a Bayesian motivation in the classical risk model, Insurance: Mathematics and Economics, 51 (2012), 370-378. doi: 10.1016/j.insmatheco.2012.06.001.

[11]

S. LiD. Landriault and C. Lemieux, A risk model with varying premiums: Its risk management implications, Insurance: Mathematics and Economics, 60 (2015), 38-46. doi: 10.1016/j.insmatheco.2014.10.010.

[12]

Z. Li and K. P. Sendova, On a ruin model with both interclaim times and premiums depending on claim sizes, Scandinavian Actuarial Journal, 2015 (2015), 245-265.

[13]

S. Loisel and J. Trufin, Ultimate ruin probability in discrete time with Buhlmann credibility premium adjustments, Bulletin Francais d'Actuariat, 13 (2013), 73-102.

[14]

C. C. -L. Tsai and G. Parker, Ruin probabilities: Classical versus credibility, NTU International Conference on Finance, 2004.

[15]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.

[16]

J.-K. Woo, A generalized penalty function for a class of discrete renewal processes, Scandinavian Actuarial Journal, 2012 (2012), 130-152.

[17]

X. Wu and S. Li, On the discounted penalty function in a discrete time renewal risk model with general interclaim times, Scandinavian Actuarial Journal, 2009 (2009), 281-294.

[18]

Z. ZhangY. Yang and C. Liu, On a perturbed compound Poisson model with varying premium rates, Journal of Industrial and Management Optimization, 13 (2017), 721-736.

show all references

References:
[1]

L. B. AfonsoA. D. Egidio dos Reis and H. R. Waters, Calculating continuous time ruin probabilities for a large portfolio with varying premium, ASTIN Bulletin, 39 (2009), 117-136. doi: 10.2143/AST.39.1.2038059.

[2]

L. B. AfonsoA. D. Egidio dos Reis and H. R. Waters, Numerical evaluation of continuous time ruin probabilities for a portfolio with credibility updated premiums, ASTIN Bulletin, 40 (2010), 399-414. doi: 10.2143/AST.40.1.2049236.

[3]

L. B. Afonso, Evaluation of ruin probabilities for surplus process with credibility and surplus dependent premium, Ph. D. Thesis, 2008.

[4]

S. Asmussen, On the ruin problem for some adapted premium rules, MaPhySto Research Report No. 5 University of Aarhus, Denmark., 1999.

[5] S. Asmussen and H. Albrecher, Ruin Probabilities, World Scientific, 2010.
[6]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, Gerber-Shiu analysis with a generalized penalty function, Scandinavian Actuarial Journal, 2010 (2010), 185-199.

[7]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, Structural properties of Gerber-Shiu function in dependent Sparre Andersen models, Insurance: Mathematics and Economics, 46 (2010), 117-126. doi: 10.1016/j.insmatheco.2009.05.009.

[8]

E. C. K. CheungD. LandriaultG. E. Willmot and J.-K. Woo, On orderings and bounds in a generalized sparre andersen risk model, Applied Stochastic Models in Business and Industry, 27 (2011), 51-60. doi: 10.1002/asmb.837.

[9]

H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal, 2 (1998), 48-78. doi: 10.1080/10920277.1998.10595671.

[10]

D. LandriaultC. Lemieux and G. E. Willmot, An adaptive premium policy with a Bayesian motivation in the classical risk model, Insurance: Mathematics and Economics, 51 (2012), 370-378. doi: 10.1016/j.insmatheco.2012.06.001.

[11]

S. LiD. Landriault and C. Lemieux, A risk model with varying premiums: Its risk management implications, Insurance: Mathematics and Economics, 60 (2015), 38-46. doi: 10.1016/j.insmatheco.2014.10.010.

[12]

Z. Li and K. P. Sendova, On a ruin model with both interclaim times and premiums depending on claim sizes, Scandinavian Actuarial Journal, 2015 (2015), 245-265.

[13]

S. Loisel and J. Trufin, Ultimate ruin probability in discrete time with Buhlmann credibility premium adjustments, Bulletin Francais d'Actuariat, 13 (2013), 73-102.

[14]

C. C. -L. Tsai and G. Parker, Ruin probabilities: Classical versus credibility, NTU International Conference on Finance, 2004.

[15]

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty, 5 (1992), 297-323.

[16]

J.-K. Woo, A generalized penalty function for a class of discrete renewal processes, Scandinavian Actuarial Journal, 2012 (2012), 130-152.

[17]

X. Wu and S. Li, On the discounted penalty function in a discrete time renewal risk model with general interclaim times, Scandinavian Actuarial Journal, 2009 (2009), 281-294.

[18]

Z. ZhangY. Yang and C. Liu, On a perturbed compound Poisson model with varying premium rates, Journal of Industrial and Management Optimization, 13 (2017), 721-736.

Figure 1.  Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 4$) ($\eta_{1}$ denotes the starting premium)
Figure 2.  Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 5$)
Figure 3.  Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 4$)
Figure 4.  Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 5$)
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