Abstract
We study the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside company and transaction costs when dividends occur. The management of the company controls the reinsurance rate, the timing and the amount of dividends paid out to maximize the expected total dividends paid out to the shareholders until ruin time. By solving the corresponding quasi-variational inequality, we obtain the optimal return function and the optimal strategy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S Asmussen, M Taksar. Controlled diffusion models for optimal dividend pay-out, Insurance Math Econom, 1997, 20: 1–15.
S Asmussen, B Højgaard, M Taksar. Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation, Finance Stoch, 2000, 4: 299–324.
A Cadenillas, T Choulli, M Taksar. Classical and impluse stochastic control for the optimization of the dividend and risk policies of an insurance firm, Math Finance, 2006, 16(1): 181–202.
T Choulli, M Taksar, X Y Zhou. An optimal diffudion model of a company with constraints on risk control, SIAM J Control Optim, 2003, 41: 1946–1979.
W H Fleming, H M Soner. Controlled Markov Process and Viscosity Solutions, Springer-Verlag, New York, 1993.
X Guo. Some risk management problems for firms with internal competition and debt, J Appl Probab, 2002, 39: 55–69.
X Guo, J Liu, X Y Zhou. Aconstrained non-linear regular-singular stochastic control problem, with applications, Stochastic Process Appl, 2004, 109: 167–187.
W H Harrison. Brownian Motion and Stochastic Flow System, John Wiley and Sons, New York, 1985.
B Højgaard, M Taksar. Controlling risk eaposure and dividends payout schemes: insurance company example, Math Finance, 1999, 2: 153–182.
B Højgaard, M Taksar. Optimal risk control for a large corporation in the presence of returns on investments, Finance Stoch, 2001, 5: 527–547.
B Højgaard, M Taksar. Optimal dynamic portfolio secetion for a corporation with controllable risk and dividend distribution policy, Quant Finance, 2004, 4: 315–327.
P Lions, A Sznitman. Stochastic differential equations with reflecting boundary conditions, Commun Pure Appl Math, 1984, 37: 511–537.
J Paulsen. Optimal dividend payouts for diffusions with solvency constraints, Finance Stoch, 2003, 4: 457–474.
M Taksar, X Y Zhou. Optimal risk and dividend control for a company with debt liability, Insurance Math Econom, 1998, 22: 105–122.
M Taksar. Optimal risk and dividend distribution control models for an insurance company, Math Methods Oper Res, 2000, 51: 1–42.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (11371284).
Rights and permissions
About this article
Cite this article
Liu, W., Hu, Yj. Optimal proportional reinsurance and dividend payments with transaction costs and internal competition. Appl. Math. J. Chin. Univ. 31, 89–102 (2016). https://doi.org/10.1007/s11766-016-3281-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11766-016-3281-7