Figure 1.
Strategy 1 ($c_{1} = 4$ and $c_{2} = 6$ ) vs Strategy 2 ($c = 4$ ) ($\eta_{1}$ denotes the starting premium)
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Optimal pricing and inventory management for a loss averse firm when facing strategic customers
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 |
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.
Keywords:
Dynamic premium,
discrete-time risk model,
Gerber-Shiu function,
geometric claims,
marketing implications.
Mathematics Subject Classification:
Primary: 60E99, 60D05.
Citation:
Wing Yan Lee, Fangda Liu. Analysis of a dynamic premium strategy: From theoretical and marketing perspectives. Journal of Industrial and Management Optimization,
2018, 14
(4)
: 1545-1564.
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.
|
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