Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-28T11:18:14.924Z Has data issue: false hasContentIssue false

OPTIMAL FINANCING AND DIVIDEND DISTRIBUTION WITH TRANSACTION COSTS IN THE CASE OF RESTRICTED DIVIDEND RATES

Published online by Cambridge University Press:  05 October 2016

Jinxia Zhu*
Affiliation:
School of Risk and Actuarial Studies, UNSW Business School, The University of New South Wales, Sydney, NSW 2031, Australia

Abstract

We consider the optimal financing (capital injections) and dividend payment problem for a Brownian motion model in the case of restricted dividend rates. The company has no obligation to inject capitals and therefore, the bankruptcy risk is present. Capital injections, if any, will incur both fixed and proportional transaction costs and dividend payments incur proportional transaction costs. The aim is to find the optimal strategy to maximize the expected present value of dividend payments minus the total cost of capital injections up to the time of bankruptcy. The problem is formulated as a mixed impulse-regular control problem. We address the problem via studying three cases of two auxiliary functions. We derive important analytical properties of the auxiliary functions and use them to study the value function and then identify the optimal control strategy. We show that the optimal dividend control is of threshold type and the optimal financing strategy prescribes to either never inject capitals or inject capitals only when the surplus reaches 0 with a fixed lump sum amount.

Type
Research Article
Copyright
Copyright © Astin Bulletin 2016 

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

Albrecher, H. and Thonhauser, S. (2009) Optimality results for dividend problems in insurance. Rev. R. Acad. Cien. Serie A. Mat., 103, 295320.Google Scholar
Asmussen, S. and Taksar, M. (1997) Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics, 20, 115.Google Scholar
Avanzi, B. (2009) Strategies for dividend distributions: A review. North American Actuarial Journal, 13, 217251.Google Scholar
Azcue, P. and Muler, N. (2012) Optimal dividend policies for compound poisson processes: The case of bounded dividend rates. Insurance: Mathematics and Economics, 51, 2642.Google Scholar
Fang, Y. and Wu, R. (2009) Optimal dividends in the Brownian motion risk model with interest. Journal of Computational and Applied Mathematics, 229, 145151.Google Scholar
He, L. and Liang, Z. (2009) Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insurance: Mathematics and Economics, 44 (1), 8894.Google Scholar
Løkka, A. and Zervos, M. (2008) Optimal dividend and issuance of equity policies in the presence of proportional costs. Insurance: Mathematics and Economics, 42, 954961.Google Scholar
Meng, H. and Siu, T.K. (2011) Impulse control of proportional reinsurance with constraints. International Journal of Stochastic Analysis, 2011, Article ID 190603.Google Scholar
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 (3), 669689.Google Scholar
Peng, X., Chen, M. and Guo, J. (2012) Optimal dividend and equity issuance problem with proportional and fixed transaction costs. Insurance: Mathematics and Economics, 51 (3), 576585.Google Scholar
Scheer, N. and Schmidli, H. (2011) Optimal dividend strategies in a Cramér-Lundberg model with capital injections and administration costs.Google Scholar
Sotomayor, L.R. and Cadenillas, A. (2011) Classical and singular stochastic control for the optimal dividend policy when there is regime switching. Insurance: Mathematics and Economics, 48 (3), 344354.Google Scholar
Taksar, M.I. (2000) Optimal risk and dividend distribution control models for insurance company. Mathematical Methods of Operations Research, 51, 142.Google Scholar
Wei, J., Yang, H. and Wang, R. (2011) Optimal threshold dividend strategies under the compound poisson model with regime switching. In Stochastic Analysis with Financial Applications (eds. Kohatsu-Higa, A., Privault, N. and Sheu, S.-J.), pp. 413429. Progress in Probability, volume 65. Basel: Springer.Google Scholar
Yao, D., Yang, H. and Wang, R. (2014) Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle. Economic Modelling, 37, 5364.Google Scholar
Zhu, J. (2014) Dividend optimization for a regime-switching diffusion model with restricted dividend rates. ASTIN Bulletin, 44, 459494.Google Scholar
Zhu, J. (2015) Dividend optimization for general diffusions with restricted dividend payment rates. Scandinavian Actuarial Journal, 2015, 592615.Google Scholar
Zhu, J. and Yang, H. (2016) Optimal financing and dividend distribution in a general diffusion model with regime switching. Advances in Applied Probability, 48, 406422.Google Scholar