We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we are able to show that for a special parameter choice the optimal strategy is a constant-barrier strategy.

中文翻译：

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在指数CIR作为折扣因子的情况下优化股息和消费

我们考虑一个经济主体（家庭或保险公司）通过确定性过程或带有漂移的布朗运动来模拟其剩余过程。目标是在指数CIR流程给出的折现系数下，最大化预期的折现支出/股息支付。在确定性的情况下，我们能够找到最佳策略和价值函数的显式表达式。对于布朗运动情况，我们能够证明，对于特殊的参数选择，最优策略是恒定势垒策略。