• Previous Article
    Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm
  • JIMO Home
  • This Issue
  • Next Article
    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

* 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.  Google Scholar

[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.  Google Scholar

[3]

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

[4]

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

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[14]

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

[15]

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

[16]

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

[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.   Google Scholar

[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.   Google Scholar

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.  Google Scholar

[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.  Google Scholar

[3]

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

[4]

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

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[14]

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

[15]

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

[16]

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

[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.   Google Scholar

[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.   Google Scholar

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 ($c = 5$)
[1]

Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183

[2]

Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973

[3]

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee. Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021035

[4]

Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623

[5]

Palash Sarkar, Subhadip Singha. Verifying solutions to LWE with implications for concrete security. Advances in Mathematics of Communications, 2021, 15 (2) : 257-266. doi: 10.3934/amc.2020057

[6]

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151

[7]

Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021

[8]

Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709

[9]

Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109

[10]

Ralf Hielscher, Michael Quellmalz. Reconstructing a function on the sphere from its means along vertical slices. Inverse Problems & Imaging, 2016, 10 (3) : 711-739. doi: 10.3934/ipi.2016018

[11]

Matthias Erbar, Jan Maas. Gradient flow structures for discrete porous medium equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1355-1374. doi: 10.3934/dcds.2014.34.1355

[12]

Xianchao Xiu, Ying Yang, Wanquan Liu, Lingchen Kong, Meijuan Shang. An improved total variation regularized RPCA for moving object detection with dynamic background. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1685-1698. doi: 10.3934/jimo.2019024

[13]

Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247

[14]

Cécile Carrère, Grégoire Nadin. Influence of mutations in phenotypically-structured populations in time periodic environment. Discrete & Continuous Dynamical Systems - B, 2020, 25 (9) : 3609-3630. doi: 10.3934/dcdsb.2020075

[15]

Guillermo Reyes, Juan-Luis Vázquez. Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. Communications on Pure & Applied Analysis, 2009, 8 (2) : 493-508. doi: 10.3934/cpaa.2009.8.493

[16]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189

[17]

Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258

[18]

Alexey Yulin, Alan Champneys. Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1341-1357. doi: 10.3934/dcdss.2011.4.1341

[19]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195

[20]

Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (177)
  • HTML views (1052)
  • Cited by (0)

Other articles
by authors

[Back to Top]