American Institute of Mathematical Sciences

• Previous Article
Optimal reinsurance and investment strategy with two piece utility function
• JIMO Home
• This Issue
• Next Article
Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs
April  2017, 13(2): 721-736. doi: 10.3934/jimo.2016043

On a perturbed compound Poisson model with varying premium rates

 1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 2 Department of Statistics, Nanjing Audit University, Nanjing 211815, China

* Corresponding author: Chaolin Liu

Received  November 2015 Revised  January 2016 Published  August 2016

Fund Project: Z.M. Zhang was supported by the National Natural Science Foundation of China [11471058,11101451,11301303] and the Natural Science Foundation Project of CQ CSTC of China [cstc2014jcyjA00007]. The research of Y. Yang was supported by National Natural Science Foundation of China (No. 71471090), the Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 14YJCZH182), China Postdoctoral Science Foundation (No. 2014T70449,2012M520964), Natural Science Foundation of Jiangsu Province of China (No. BK20131339), the Major Research Plan of Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 15KJA110001), Qing Lan Project, PAPD, Program of Excellent Science and Technology Innovation Team of the Jiangsu Higher Education Institu-tions of China, Project of Construction for Superior Subjects of Statistics of Jiangsu Higher Education Institutions, Project of the Key Lab of Financial Engineering of Jiangsu Province. The research of C.L. Liu was supported by the Fundamental Research Funds for the Central Universities(No. 106112015CDJXY100006).

In this paper, we consider a perturbed compound Poisson model with varying premium rates. The surplus process is observed at a sequence of review times. The effective premium rate is adjusted according to the surplus increment between the inter-review times. We study the Gerber-Shiu functions by Laplace transform method. When the claim size density is a combination of exponentials, the explicit expressions for the Laplace transforms of ruin time are derived.

Citation: Zhimin Zhang, Yang Yang, Chaolin Liu. On a perturbed compound Poisson model with varying premium rates. Journal of Industrial & Management Optimization, 2017, 13 (2) : 721-736. doi: 10.3934/jimo.2016043
References:

show all references

References:
Ruin probabilities for Erlang(2) inter-review times. (a) $f_X(x)=3e^{-1.5x}-3 e^{-3x}$; (b) $f_X(x)=e^{-x}$; (c) $f_X(x)=\frac{1}{6} e^{-\frac{1}{2}x}+\frac{4}{3} e^{-2x}$
Exact values of ruin probabilities when $f_X(x)=\frac{1}{6} e^{-\frac{1}{2}x}+\frac{4}{3} e^{-2x}$
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.64215 0.33207 0.15448 0.06979 0.03119 0.01388 0.00617 0.00274 0.00121 0.00054 $\phi_2(u)$ 0.41629 0.19545 0.08830 0.03946 0.01757 0.00781 0.00347 0.00154 0.00068 0.00030
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.64215 0.33207 0.15448 0.06979 0.03119 0.01388 0.00617 0.00274 0.00121 0.00054 $\phi_2(u)$ 0.41629 0.19545 0.08830 0.03946 0.01757 0.00781 0.00347 0.00154 0.00068 0.00030
Exact values of ruin probabilities when $f_X(x)=e^{-x}$
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.70195 0.42231 0.23766 0.13018 0.07048 0.03797 0.02041 0.01096 0.00588 0.00316 $\phi_2(u)$ 0.48671 0.27859 0.15357 0.08339 0.04500 0.02421 0.01301 0.00699 0.00375 0.00201
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.70195 0.42231 0.23766 0.13018 0.07048 0.03797 0.02041 0.01096 0.00588 0.00316 $\phi_2(u)$ 0.48671 0.27859 0.15357 0.08339 0.04500 0.02421 0.01301 0.00699 0.00375 0.00201
Exact values of ruin probabilities when $f_X(x)=\frac{1}{6} e^{-\frac{1}{2}x}+\frac{4}{3} e^{-2x}$
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.75332 0.55726 0.40147 0.28352 0.19789 0.13718 0.09472 0.06524 0.04488 0.03084 $\phi_2(u)$ 0.59185 0.43080 0.30693 0.21544 0.14989 0.10374 0.07158 0.04929 0.03390 0.02330
 $u$ $0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $\phi_1(u)$ 0.75332 0.55726 0.40147 0.28352 0.19789 0.13718 0.09472 0.06524 0.04488 0.03084 $\phi_2(u)$ 0.59185 0.43080 0.30693 0.21544 0.14989 0.10374 0.07158 0.04929 0.03390 0.02330
 [1] Prasanta Kumar Barik, Ankik Kumar Giri, Rajesh Kumar. Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021009 [2] 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 [3] 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 [4] 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 [5] Dayalal Suthar, Sunil Dutt Purohit, Haile Habenom, Jagdev Singh. Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021019 [6] Saima Rashid, Fahd Jarad, Zakia Hammouch. Some new bounds analogous to generalized proportional fractional integral operator with respect to another function. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021020

2019 Impact Factor: 1.366