Capital injections with negative surplus and delays:models and analysis
Zhuo JIN
George YIN
摘要：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.
机标关键词：value functiondynamic programmingstochastic controlinjection barriersurplus processtime delaysnew modeldeal with
资助基金：The research of Z. Jin was supported by the Faculty Research Grant of University of Melbourne, and the research of G. Yin was partial y supported by the National Science Foundation (DMS-1207667)
论文发表日期：2014-01-01
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：10( 163-172 )
英文信息