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Optimal control of a big financial company with debt liability under bankrupt probability constraints

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  • Zongxia Liang
  • Bin Sun

Abstract

This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to choose various production/business policies from an available set of control policies with different expected profits and risks, controls the business policy and dividend payout process to maximize the expected present value of the dividends until the time of bankruptcy. However, if the dividend payout barrier is too low to be acceptable, it may result in the company's bankruptcy soon. In order to protect the shareholders' profits, the managements of the company impose a reasonable and normal constraint on their dividend strategy, that is, the bankrupt probability associated with the optimal dividend payout barrier should be smaller than a given risk level within a fixed time horizon. This paper aims at working out the optimal control policy as well as optimal return function for the company under bankrupt probability constraint by stochastic analysis, PDE methods and variational inequality approach. Moreover, we establish a risk-based capital standard to ensure the capital requirement of can cover the total given risk by numerical analysis and give reasonable economic interpretation for the results.

Suggested Citation

  • Zongxia Liang & Bin Sun, 2010. "Optimal control of a big financial company with debt liability under bankrupt probability constraints," Papers 1007.5376, arXiv.org, revised Aug 2010.
    • Handle: RePEc:arx:papers:1007.5376
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    References listed on IDEAS

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    1. He, Lin & Liang, Zongxia, 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 88-94, February.
    2. He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
    3. Bjarne Højgaard & Michael Taksar, 2001. "Optimal risk control for a large corporation in the presence of returns on investments," Finance and Stochastics, Springer, vol. 5(4), pages 527-547.
    4. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    5. Guo, Xin & Liu, Jun & Zhou, Xun Yu, 2004. "A constrained non-linear regular-singular stochastic control problem, with applications," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 167-187, February.
    6. He, Lin & Hou, Ping & Liang, Zongxia, 2008. "Optimal control of the insurance company with proportional reinsurance policy under solvency constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 474-479, December.
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