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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, doi: 10.3934/jimo.2018020
##### References:
 [1] L. B. Afonso, A. 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. Afonso, A. 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. Cheung, D. Landriault, G. 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. Cheung, D. Landriault, G. 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. Cheung, D. Landriault, G. 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. Landriault, C. 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. Li, D. 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. Zhang, Y. 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. Afonso, A. 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. Afonso, A. 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. Cheung, D. Landriault, G. 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. Cheung, D. Landriault, G. 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. Cheung, D. Landriault, G. 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. Landriault, C. 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. Li, D. 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. Zhang, Y. Yang and C. Liu, On a perturbed compound Poisson model with varying premium rates, Journal of Industrial and Management Optimization, 13 (2017), 721-736.
Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 4$) ($\eta_{1}$ denotes the starting premium)
Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 5$)
Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 4$)
Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$) vs Strategy 2 ($c = 5$)
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