Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T21:34:24.677Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL DIVIDEND–REINSURANCE WITH TWO TYPES OF PREMIUM PRINCIPLES

Published online by Cambridge University Press:  09 December 2015

Hui Meng ,
Ming Zhou  and
Tak Kuen Siu
Hui Meng
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, People's Republic of China E-mail: menghuidragon@126.com
Ming Zhou
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, People's Republic of China E-mail: mzhou.act@gmail.com
Tak Kuen Siu
Affiliation:
Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia E-mail: Ken.Siu@mq.edu.au; ktksiu2005@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A combined optimal dividend/reinsurance problem with two types of insurance claims, namely the expected premium principle and the variance premium principle, is discussed. Dividend payments are considered with both fixed and proportional transaction costs. The objective of an insurer is to determine an optimal dividend–reinsurance policy so as to maximize the expected total value of discounted dividend payments to shareholders up to ruin time. The problem is formulated as an optimal regular-impulse control problem. Closed-form solutions for the value function and optimal dividend–reinsurance strategy are obtained in some particular cases. Finally, some numerical analysis is given to illustrate the effects of safety loading on optimal reinsurance strategy.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 2 , April 2016 , pp. 224 - 243
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Alvarez, L.H.R. & Lempa, J. (2008). On the optimal stochastic impulse control of linear diffusion. SIAM Journal of Control Optimization 47(2): 703–732.Google Scholar
2.Asmussen, S. & Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics 20(1): 1–15.Google Scholar
3.Asmussen, S., Højgaard, B., & Taksar, M. (2000). Optimal risk control and dividend distribution policies. Example of excess of loss reinsurance for an insurance corporation. Finance and Stochastics l4(3): 299–324.Google Scholar
4.Bai, L.H. & Guo, J.Y. (2010). Optimal dividend payments in the classical risk model when payments are subject to both transaction costs and taxes. Scandinavian Actuarial Journal 1: 36–55.CrossRefGoogle Scholar
5.Cadenillas, A., Choulli, T., Taksar, M., & Zhang, L. (2006). Classical and impulse stochastic control for the optimization of the dividend and risk policies of an insurance firm. Mathematical Finance 16(1): 181–202.CrossRefGoogle Scholar
6.Choulli, T., Taksar, M., & Zhou, X.Y. (2001). Excess of loss reinsurance for a company with debt liability and constraints on risk reduction. Quantitative Finance 1: 573–596.Google Scholar
7.Choulli, T., Taksar, M., & Zhou, X.Y. (2003). A diffusion model for optimal dividend distribution for a company with constraints on risk control. SIAM Journal of Control Optimization 41(6): 1946–1979.Google Scholar
8.De Finetti, B. (1957). Su unimpostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries 2: 433–443.Google Scholar
9.Fleming, W.H. & Rishel, R.W. (1975). Deterministic and stochastic optimal control. New York: Springer.Google Scholar
10.Gerber, H.U. (1972). Games of economic survival with discrete continuous income processes. Operations Research 20(1): 37–45.Google Scholar
11.Gerber, H.U. & Shiu, E.S.W. (2004). Optimal dividends: analysis with Brownian motion. North American Actuarial Journal 8(1): 1–20.Google Scholar
12.Grandell, J. (1991). Aspects of risk theory. New York: Springer.Google Scholar
13.Hipp, C. & Taksar, M. (2010). Optimal non-proportional reinsurance control. Insurance: Mathematics and Economics 47(2): 246–254.Google Scholar
14.Højgaard, B. & Taksar, M. (1999). Controlling risk exposure and dividends payout schemes: Insurance company example, Mathematical Finance 9(2): 153–182.CrossRefGoogle Scholar
15.Meng, H. & Zhang, X. (2010). Optimal risk control for the excess of loss reinsurance polices. ASTIN Bulletin 40(1): 179–197.Google Scholar
16.Meng, H. & Siu, T.K. (2011). On optimal reinsurance, dividend and reinvestment strategies. Economic Modelling 28(1–2): 211–218.Google Scholar
17.Meng, H. & Siu, T.K. (2011). Optimal mixed impulse-equity insurance control problem with reinsurance. SIAM Journal of Control Optimization 49(1): 254–279, 1946–1979.CrossRefGoogle Scholar
18.Meng, H. & Siu, T.K. (2011). Impulse control of proportional reinsurance with constraints. International Journal of Stochastic Analysis Volume 2011, Article ID 190603, 13 pages. DOI:10.1155/2011/190603.CrossRefGoogle Scholar
19.Meng, H. (2013). Optimal impulse control with variance premium principle (in Chinese). Scientia Sinica Mathematica 43: 925–939.Google Scholar
20.Meng, H., Siu, T.K., & Yang, H.L. (2013). Optimal dividends with debts and nonlinear insurance risk processes. Insurance: Mathematics and Economics 53: 110–121.Google Scholar
21.Meng, H., Siu, T.K., & Yang, H.L. (2015). Optimal insurance risk control with multiple reinsurance. Submitted.Google Scholar
22.Meng, H., Zhou, M., & Siu, T.K. (2015). Optimal reinsurance policies with two reinsurers in continuous time. Submitted.Google Scholar
23.Ormeci, M., Dai, J., & Vate, J. (2008). Impulse control of Brownian motion: the constrained average cost case. Operations Research 56(3): 618–629.CrossRefGoogle Scholar
24.Paulsen, J. (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics 7(4): 457–473.Google Scholar
25.Paulsen, J. (2007). Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs. Advances in Applied Probability 39(1): 669–689.CrossRefGoogle Scholar
26.Schmidli, H. (2001). Optimal proportional reinsurance polices in dynamic setting. Scandinavian Actuarial Journal 1: 55–68.Google Scholar
27.Schmidli, H. (2002). On minimizing the ruin probability by investment and reinsurance. The Annals of Applied Probability 12: 890–907.Google Scholar
28.Taksar, M. (2000). Optimal risk and dividend distribution control models for an insurance company. Mathematical Methods of Operational Research 51: 1–42.Google Scholar
29.Taksar, M. & Markussen, C. (2003). Optimal dynamic reinsurance policies for large insurance portfolios. Finance and Stochastics 7: 97–121.Google Scholar
30.Zhou, M. & Cai, J. (2014). Optimal dynamic risk control for insurers with state dependent income. Journal of Applied Probability 51: 417–435.Google Scholar
31.Zhou, M. & Yiu, K.F.C. (2014). Optimal dividend strategy with transaction costs for an upward jump model. Quantitative Finance 14: 1097–1106.Google Scholar
32.Zhou, M. & Yuen, K.C. (2012). Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle. Economic Modelling 29: 198–207.Google Scholar