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Optimal dividends and capital injection under dividend restrictions
Mathematical Methods of Operations Research ( IF 1.2 ) Pub Date : 2020-07-16 , DOI: 10.1007/s00186-020-00720-y
Kristoffer Lindensjö , Filip Lindskog

We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection. We show that one of the following strategies is optimal: (i) Pay dividends and inject capital in order to reflect the surplus process at an upper barrier and at 0, implying bankruptcy never occurs. (ii) Pay dividends in order to reflect the surplus process at an upper barrier and never inject capital—corresponding to absorption at 0—implying bankruptcy occurs the first time the surplus reaches zero. We show that if the costs of capital injection are low, then a sufficiently high dividend payout barrier will change the optimal strategy from type (i) (without bankruptcy) to type (ii) (with bankruptcy). Moreover, if the costs are high, then the optimal strategy is of type (ii) regardless of the dividend payout barrier. We also consider the possibility for the owner to choose a stopping time at which the insurance company is liquidated and the owner obtains a liquidation value. The uncontrolled surplus process is a Wiener process with drift.



中文翻译:

股息限制下的最优股息和注资

我们研究了一家保险公司的所有者所面临的奇异的随机控制问题,该所有者在存在盈余过程必须高于给定的股息支付障碍的限制的情况下动态地支付股息并筹集资金为了允许股息支付。如果盈余过程变为负数且注资有成比例的成本,就会发生破产。我们表明,以下策略之一是最佳的:(i)支付股息并注入资本,以在盈余上限和0处反映盈余过程,这意味着从未发生破产。(ii)支付股息以反映盈余过程处于较高的障碍,并且从不注入资本(对应于0的吸收率),这意味着破产是在盈余首次达到零时发生的。我们表明,如果注资成本较低,那么足够高的股息支付壁垒将使最佳策略从(i)类型(无破产)变为(ii)类型(破产)。而且,如果成本很高,则最佳策略为(ii)类型,与股息支付障碍无关。我们还考虑了所有者选择保险公司清算的停止时间以及所有者获得清算价值的可能性。不受控制的剩余过程是带有漂移的维纳过程。

更新日期:2020-07-16
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