Optimal dividend payout under stochastic discounting
Optimal dividend payout under stochastic discounting
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DOI：
10.1111/mafi.12339
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发表时间：
2020-05
影响因子：
1.6
通讯作者：
Elena Bandini;T. Angelis;Giorgio Ferrari;Fausto Gozzi
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文献类型：
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作者：
Elena Bandini;T. Angelis;Giorgio Ferrari;Fausto Gozzi
本文采用概率方法确定了盈余过程遵循受控的算法布朗运动且现金流以随机动态折现率贴现的企业的最优股利支付政策。股息可以不受限制地支付给股东，因此问题被视为一个奇异随机控制问题。随机利率由Cox-Ingersoll-Ross （CIR）过程建模，公司的目标是最大化贴现股息的总预期流量，直到可能的破产时间。我们找到了一个最优股利支付策略，它使得盈余过程保持在一个内源性确定的随机阈值以下，该阈值表示为当前利率值的递减连续函数r∈b(r)$r\映射到b(r)$。我们还证明了奇异控制问题的值函数解决了与二阶非退化椭圆算子相关的一个带梯度约束的变分不等式。
Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash‐flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modeled by a Cox–Ingersoll–Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time. We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing continuous function r↦b(r)$r\mapsto b(r)$ of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second‐order, non‐degenerate elliptic operator, with a gradient constraint.