In this paper we provide a stock price model that explicitly incorporates credit risk, under a stochastic optimal control system. The stock price model also incorporates the managerial control of credit risk through a control policy in the stochastic system. We provide explicit conditions on the existence of optimal feedback controls for the stock price model with credit risk. We prove the continuity of the value function, and then prove the dynamic programming principle for our system. Finally, we prove the Viscosity Solution of the Hamilton–Jacobi–Bellman equation. This paper is particularly relevant to industry, as the impact of credit risk upon stock prices has been prominent since the commencement of the Global Financial Crisis.

在本文中，我们提供了一种在随机最优控制系统下明确包含信用风险的股票价格模型。股票价格模型还通过随机系统中的控制策略合并了对信用风险的管理控制。我们为存在信用风险的股票价格模型的最优反馈控制的存在提供了明确的条件。我们证明了值函数的连续性，然后证明了我们系统的动态编程原理。最后，我们证明了Hamilton–Jacobi–Bellman方程的粘度解。自全球金融危机爆发以来，信用风险对股票价格的影响一直很突出，因此本文与行业特别相关。