带借贷利率的复合泊松模型的脉冲分红与注资问题
Impulse Dividend and Capital Injection Problem in the Compound Poisson Model with Debit Interest
摘要: 本文研究了带借贷利率的复合泊松模型的脉冲分红与注资问题。本文目标是最大化绝对破产界之上分红现值与注资现值之差的期望值。我们先得到值函数的性质，给出可行策略的定义，然后根据随机控制理论证明了动态规划原理，启发式得出QVI不等式并且证明值函数是该不等式的几乎处处解，最后在最优策略存在的前提下给出验证定理的证明。
Abstract: In this paper, we study the problem of impulse dividend and capital injection in the compound Poisson model with debit interest. The objective is to maximize the expected present value of the dividends minus the discounted costs of capital injections until the absolute bankruptcy boundary. Firstly, we get the properties of the value function and give the definition of the admissible strategy. Then, we prove the dynamic programming principle according to the stochastic control theory, elicit the QVI inequality and prove that the value function is almost everywhere solution of the inequality. Finally, we give the proof of the verification theorem on the premise of the existence of the optimal strategy.
文章引用：罗彬. 带借贷利率的复合泊松模型的脉冲分红与注资问题[J]. 应用数学进展, 2023, 12(3): 980-992. https://doi.org/10.12677/AAM.2023.123100

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