# American Institute of Mathematical Sciences

• Previous Article
Optimal pricing and inventory management for a loss averse firm when facing strategic customers
• JIMO Home
• This Issue
• Next Article
Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm
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:

show all references

##### References:
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 ($c = 5$)
 [1] Abhyudai Singh, Roger M. Nisbet. Variation in risk in single-species discrete-time models. Mathematical Biosciences & Engineering, 2008, 5 (4) : 859-875. doi: 10.3934/mbe.2008.5.859 [2] Qingwu Gao, Zhongquan Huang, Houcai Shen, Juan Zheng. Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims. Journal of Industrial & Management Optimization, 2016, 12 (1) : 31-43. doi: 10.3934/jimo.2016.12.31 [3] Yuebao Wang, Qingwu Gao, Kaiyong Wang, Xijun Liu. Random time ruin probability for the renewal risk model with heavy-tailed claims. Journal of Industrial & Management Optimization, 2009, 5 (4) : 719-736. doi: 10.3934/jimo.2009.5.719 [4] Rongfei Liu, Dingcheng Wang, Jiangyan Peng. Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times. Journal of Industrial & Management Optimization, 2017, 13 (2) : 995-1007. doi: 10.3934/jimo.2016058 [5] H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183 [6] Eduardo Liz. A new flexible discrete-time model for stable populations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2487-2498. doi: 10.3934/dcdsb.2018066 [7] Martino Bardi, Shigeaki Koike, Pierpaolo Soravia. Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 361-380. doi: 10.3934/dcds.2000.6.361 [8] Sie Long Kek, Mohd Ismail Abd Aziz, Kok Lay Teo, Rohanin Ahmad. An iterative algorithm based on model-reality differences for discrete-time nonlinear stochastic optimal control problems. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 109-125. doi: 10.3934/naco.2013.3.109 [9] Yun Kang. Permanence of a general discrete-time two-species-interaction model with nonlinear per-capita growth rates. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2123-2142. doi: 10.3934/dcdsb.2013.18.2123 [10] Ka Chun Cheung, Hailiang Yang. Optimal investment-consumption strategy in a discrete-time model with regime switching. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 315-332. doi: 10.3934/dcdsb.2007.8.315 [11] Agnieszka B. Malinowska, Tatiana Odzijewicz. Optimal control of the discrete-time fractional-order Cucker-Smale model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 347-357. doi: 10.3934/dcdsb.2018023 [12] Ferenc A. Bartha, Ábel Garab. Necessary and sufficient condition for the global stability of a delayed discrete-time single neuron model. Journal of Computational Dynamics, 2014, 1 (2) : 213-232. doi: 10.3934/jcd.2014.1.213 [13] Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discrete-time systems. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 329-337. doi: 10.3934/naco.2016015 [14] Sie Long Kek, Kok Lay Teo, Mohd Ismail Abd Aziz. Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 207-222. doi: 10.3934/naco.2012.2.207 [15] John E. Franke, Abdul-Aziz Yakubu. Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences & Engineering, 2011, 8 (2) : 385-408. doi: 10.3934/mbe.2011.8.385 [16] S. R.-J. Jang. Allee effects in a discrete-time host-parasitoid model with stage structure in the host. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 145-159. doi: 10.3934/dcdsb.2007.8.145 [17] Sie Long Kek, Mohd Ismail Abd Aziz. Output regulation for discrete-time nonlinear stochastic optimal control problems with model-reality differences. Numerical Algebra, Control & Optimization, 2015, 5 (3) : 275-288. doi: 10.3934/naco.2015.5.275 [18] Dan Zhang, Xiaochun Cai, Lin Wang. Complex dynamics in a discrete-time size-structured chemostat model with inhibitory kinetics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3439-3451. doi: 10.3934/dcdsb.2018327 [19] Yinghua Dong, Yuebao Wang. Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums. Journal of Industrial & Management Optimization, 2011, 7 (4) : 849-874. doi: 10.3934/jimo.2011.7.849 [20] Yang Yang, Kaiyong Wang, Jiajun Liu, Zhimin Zhang. Asymptotics for a bidimensional risk model with two geometric Lévy price processes. Journal of Industrial & Management Optimization, 2019, 15 (2) : 481-505. doi: 10.3934/jimo.2018053

2017 Impact Factor: 0.994

## Tools

Article outline

Figures and Tables