
Optimization of risk policy and dividends with fixed transaction costs under interest rate
Xin ZHANG, Min SONG
Front. Math. China ›› 2012, Vol. 7 ›› Issue (4) : 795-811.
Optimization of risk policy and dividends with fixed transaction costs under interest rate
In this paper, we consider the dividend optimization problem for a financial corporation with transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and the surplus earns interest at the constant force ρ>0. Because of the presence of fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy.
Mixed classical-impulse control / impulse control / dividends / quasivariational inequality / transaction costs
[1] |
Abramowitz M, Stegun I A. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Washington: United States Department of Commerce, US Government Printing Office, 1972
|
[2] |
Asmussen S, Højgaard B, Taksar M. Optimal risk control and dividend distribution policies: Example of excess-of loss reinsurance for an insurance corporation. Finance Stoch, 2000, 4(3): 299-324
CrossRef
Google scholar
|
[3] |
Asmussen S, Taksar M. Controlled diffusion models for optimal dividend pay-out. Insurance Math Econom, 1997, 20(1): 1-15
CrossRef
Google scholar
|
[4] |
Bensoussan A, Lions J L. Nouvelle formulation de problèmes de contrôle impulsionnel et applications. C R Acad Sci Paris Sér A-B, 1973, 276: 1189-1192
|
[5] |
Bensoussan A, Lions J L. Impulse Control and Quasivariational Inequalities. Montrouge: Gauthier-Villars, Montrouge, 1984
|
[6] |
Cadenillas A. Consumption-investment problems with transaction costs: survey and open problems. Math Methods Oper Res, 2000, 51(1): 43-68
CrossRef
Google scholar
|
[7] |
Cadenillas A, Choulli T, Taksar M, Zhang L. Classical and impulse stochastic control for the optimization of the dividend and risk policies of an insurance firm. Math Finance, 2006, 16(1): 181-202
CrossRef
Google scholar
|
[8] |
Cadenillas A, Zapatero F. Classical and impulse stochastic control of the exchange rate using interest rates and reserves. Math Finance, 2000, 10(2): 141-156
CrossRef
Google scholar
|
[9] |
Cai J, Gerber H U, Yang H. Optimal dividends in an Ornstein-Uhlenbeck type model with credit and debit interest. North Amer Actuar J, 2006, 10(2): 94-119
|
[10] |
Choulli T, Taksar M, Zhou X Y. Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction. Quant Finance, 2001, 1(6): 573-596
CrossRef
Google scholar
|
[11] |
Choulli T, Taksar M, Zhou X Y. A diffusion model for optimal dividend distribution for a company with constraints on risk control. SIAM J Control Optim, 2003, 41(6): 1946-1979
CrossRef
Google scholar
|
[12] |
Dixit A. A simplified treatment of the theory of optimal regulation of Brownian motion. J Econom Dynam Control, 1991, 15(4): 657-673
CrossRef
Google scholar
|
[13] |
Dumas B. Super contact and related optimality conditions. J Econom Dynam Control, 1991, 15(4): 675-685
CrossRef
Google scholar
|
[14] |
Harrison J, Sellke T, Taylor A. Impulse Control of Brownian Motion. Math Oper Res, 1983, 8(3): 454-466
CrossRef
Google scholar
|
[15] |
Højgaard B, Taksar M. Optimal proportional reinsurance policies for diffusion models. Scand Actuar J, 1998, 2: 166-180
|
[16] |
Højgaard B, Taksar M. Controlling risk exposure and dividends payout schemes: insurance company example. Math Finance, 1999, 9(2): 153-182
CrossRef
Google scholar
|
[17] |
Højgaard B, Taksar M. Optimal risk control for a large corporation in the presence of returns on investments. Finance Stoch, 2001, 5(4): 527-547
CrossRef
Google scholar
|
[18] |
Højgaard B, Taksar M. Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy. Quant Finance, 2004, 4(3): 315-327
CrossRef
Google scholar
|
[19] |
Jeanblanc-Picque M, Shiryaev A. Optimization of the flow of dividends. Russian Math Surveys, 1995, 50(2): 257-277
CrossRef
Google scholar
|
[20] |
Korn R. Optimal inpulse control when control actions have random consequences. Math Oper Res, 1997, 22(3): 639-667
CrossRef
Google scholar
|
[21] |
Korn R. Portfolio optimisation with strictly positive transaction costs and impulse control. Finance Stoch, 1998, 2(2): 85-114
CrossRef
Google scholar
|
[22] |
Richard S. Optimal impulse control of a diffusion process with both fixed and proportional costs of control. In: 1976 IEEE Conference on Decision and Control Including the 15th Symposium on Adaptive Processes. 1976, 759-763
|
[23] |
Taksar M. Optimal risk and dividend distribution control models for an insurance company. Math Methods Oper Res, 2000, 51(1): 1-42
CrossRef
Google scholar
|
[24] |
Yang R C, Liu K H, Xia B. Optimal impulse and regular control strategies for proportional reinsurance problem. J Appl Math Comput, 2005, 18(1-2): 145-158
CrossRef
Google scholar
|
/
〈 |
|
〉 |