We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on semiconvexity arguments, we prove that the value function is a classical solution to the associated quasi-variational inequality. This enables us to characterize the structure of the continuation and action regions and construct an optimal control. Finally, we focus on the linear case, discussing, by a numerical analysis, the sensitivity of the solution with respect to the relevant parameters of the problem.

中文翻译：

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具有固定调整成本的不可逆投资：一种随机脉冲控制方法

考虑具有固定调整成本的不可逆投资选择模型，我们考虑了无限时间范围内的最优随机脉冲控制问题。通过采用粘度解的技术并依靠半凸论点，我们证明了值函数是相关准变分不等式的经典解。这使我们能够表征连续区域和动作区域的结构，并构建最佳控制。最后，我们关注线性情况，通过数值分析来讨论解决方案相对于问题相关参数的敏感性。