基于MAP风险模型的最优分红问题研究

Abstract

Abstract:

In this paper, we model the surplus process of the insurance by the classical compound Poisson risk model modulated by an continuous-time Markov chain, which is the phase process of a Markovian Arrival Process(MAP). The surplus process can't be observed continuously. The observation and the possible dividend are restricted to a sequence of random discrete time points which are determined by the same MAP. The insurance has only observation opportunities at some of these random time points, and has both observation and paying dividend opportunities at the other random time points. The object of the insurance is to select the dividend strategy that maximizes the expected total discounted dividend payments until ruin. The purpose of this paper is to analyze the impact of the paying dividend opportunity and the economic state on the value functions and dividend strategies. We show that the optimal dividend pay-out policy is a band policy at dividend pay-out times.

Key words: Discounted dividend payments, Randomized observation periods, MAP, Bellman equation

CLC Number:

O211.9

Chen Xu, Yang Xiangqun. Optimal Dividend-Payout in a MAP Risk Model[J].Acta mathematica scientia,Series A, 2016, 36(1): 176-186.

Trendmd

References

[1] Finetti B De. Su un' impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth Congress of Actuaries, 1957, 2:433-443
[2] Gao S, Liu Z M. The perturbed compound Poisson risk model with constant interest and a threshold strategy. Journal of Computational and Applied Mathematics, 2010, 233:2181-2188
[3] Lin S X, Pavlova K P. The compound Poisson risk model with a threshold dividend strategy. Insurance Math Econom, 2006, 38:57-80
[4] Chen X, Ou H. A compound Poisson model with proportional investment. Journal of Computational and Applied Mathematics, 2013, 242:248-260
[5] Loeffen R, Renaud J. De Fineti's optimal dividends problem with an affine penalty function at ruin. Insurance Math Econom, 2010, 46(1):98-108
[6] Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model:the discounted penalty function. Scandinavian Actuarial Journal, 2013, 2013(6):424-452
[7] Albrecher H, Cheung E C K, Thonhauser S. Randomized observation periods for the compound Poisson risk model:Dividends. ASTIN Bulletion, 2011, 41(2):645-672
[8] Albrecher H, Bäuerle N, Thonhauser S. Optimal dividend-payout in random discrete time. Statistics and Risk Modeling, 2011, 28:251-276
[9] Cheung C K Eric, Landriault D. Perturbed MAP risk models with dividend barrier strategies. Journal of Applied Probability, 2009, 46(2):521-541
[10] Cheung C K Eric, Landriault D. A generallized penalty function with the maximum surplus prior to ruin in a MAP risk model. Insurance:Mathematics and Economics, 2010, 46(1):127-134
[11] Zhang Z, Yang H L, Yang H. On the absolute ruin in a MAP risk model with debit interest. Advances in Applied Probability, 2011, 43(1):77-96
[12] Mitric I R, Badescu A L, Stanford D A. On the absolute ruin problem in a Sparre Andersen risk model with constant interest. Insurance:Mathematics and Economics, 2012, 50:167-178
[13] Salah Z B, Morales M. Lévy systems and the time value of ruin for Markov additive processes. European Actuarial Journal, 2012, 2(2):289-317
[14] Bäuerler N, Rieder U. Markov Dicision Processes with Applications to Finance. New York:Springer, 2011

Metrics

Viewed

Full text

159

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	159

From	Others	local

Times	2	157
Rate	1%	99%

Abstract

152

Just accepted	Online first	Issue

0	0	152

From	Others	local

Times	108	44
Rate	71%	29%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	Yang Lichun, An Runling. Lie Derivable Maps on von Neumann Algebras [J]. Acta mathematica scientia,Series A, 2018, 38(5): 864-872.
[2]	Huang Ziyan, Zhao Di, Li Hongyi. The Schwarz-Pick Lemma for Bounded Pluriharmonic Mappings in the Unit Ball of Cⁿ [J]. Acta mathematica scientia,Series A, 2018, 38(3): 433-445.
[3]	Liu Ying. The General Iterative Algorithms for Variational Inclusions and Fixed Point Problems Extended to Banach Spaces Without the Weakly Sequentially Continuous Duality Mapping [J]. Acta mathematica scientia,Series A, 2018, 38(2): 244-263.
[4]	Xia Hongchuan, Liu Hao, Zhong Chunping. A New Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(4): 637-646.
[5]	Chen Lin. Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type [J]. Acta mathematica scientia,Series A, 2017, 37(4): 671-683.
[6]	You Lingyun, Tan Jiyang, Li Ziqiang, Zhang Hanjun. Optimal Dividend Strategy in Compound Binomial Dual Model with Bounded Dividend Rates and Periodic Dividend Payments [J]. Acta mathematica scientia,Series A, 2017, 37(4): 751-766.
[7]	Lu Jin. A Note on Distortion Theorem for Biholomorphic Convex Mappings on the Unit Ball [J]. Acta mathematica scientia,Series A, 2017, 37(3): 528-533.
[8]	Liu Aichao, Cui Yanyan, Liu Hao. The Distortion Estimation for Strongly Spirallike Mappings of Type α Along Unit Direction [J]. Acta mathematica scientia,Series A, 2017, 37(2): 239-247.
[9]	Zhang Yufang, Xu Qinghua. Refinement of Schwarz Lemma for the Modulus of Holomorphic Mappings on the Unit Disk [J]. Acta mathematica scientia,Series A, 2017, 37(1): 18-25.
[10]	Fu Xi, Lu Bowen. Some Characterizations of Bloch-type Spaces [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1040-1047.
[11]	Qi Yi, Shi Qingtian. Estimations of Convexity Radius and the Norm of Pre-Schwarz Derivative for Close to Convex Harmonic Mappings [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1057-1066.
[12]	Sun Yun, Wu Jianguang, Wang Dong, Tang Xubing. New Differential Formulae Related to Hermite Polynomials and Their Applications in Quantum Optics [J]. Acta mathematica scientia,Series A, 2016, 36(4): 795-808.
[13]	Wei Yanan, Ji Guoxing. Maps Preserving Partial Isometries of Operator Pencils [J]. Acta mathematica scientia,Series A, 2016, 36(3): 413-424.
[14]	Wang Chaojun, Cui Yanyan, Liu Hao. Generalized Roper-Suffridge Extension Operators and Loewner Chains [J]. Acta mathematica scientia,Series A, 2016, 36(3): 433-440.
[15]	Wei Dongyi. Exact Number of Solutions of a One-Dimensional Prescribed Mean Curvature Equation with General Nonlinearities [J]. Acta mathematica scientia,Series A, 2016, 36(1): 1-13.

Optimal Dividend-Payout in a MAP Risk Model

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10