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Capital injections with negative surplus and delays: models and analysis

control Theory and Technology 2014年第2期12卷 163-172页

作者： Zhuo JIN George YIN Centre for Actuarial Studies Department of Economics The University of Melbourne VIC 3010 Australia Department of Mathematics Wayne State University Detroit Michigan 48202 U.S.A.

This work develops a new model to deal with the scenario that some companies can still run business even the surplus falls below zero temporarily. With such a scenario in mind, we allow the surplus process to continue in this negative-surplus period, during which capital injections will be ordered to assist in the stabilization of financial structure, until the financial status becomes severe enough to file bankruptcy. The capital injections will be modeled as impulse controls. By introducing the capital injections with time delays, optimal dividend payment and capital injection policies are considered. Using the dynamic programming approach, the value function obeys a quasi-variational inequality. With delays in capital injections, the company will be exposed to the risk of bankruptcy during the delay period. In addition, the optimal dividend payment and capital injection strategies should balance the expected cost of the possible capital injections and the time value of the delay periods. This gives rise to a stochastic control problem with mixed singular and delayed impulse controls. Under general assumptions, the lower capital injection barrier is determined, where bankruptcy occurs. The closed-form solution to the value function and corresponding optimal policies are obtained.

关键词： Stochastic control Capital injection Dividend policy delayed impulse control Singular contro

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