英文标题：
《Numerical approximation of a cash-constrained firm value with investment
opportunities》
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作者：
Erwan Pierre, St\\\'ephane Villeneuve, Xavier Warin
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最新提交年份：
2016
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英文摘要：
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deterministic approximation of the related HJB variational inequality is provided. We finally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies.
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中文摘要：
我们考虑了一个带有制度转换的奇异控制问题，该问题出现在现金约束企业的最优投资决策问题中。证明了该值函数是关联的Hamilton-Jacobi-Bellman方程的唯一粘性解。此外，我们还给出了值函数的正则性以及控制区域形状的描述。基于这些理论结果，给出了相关HJB变分不等式的数值确定性近似。最后，我们证明了这种数值逼近收敛到值函数。这使我们能够描述投资和股息的最优政策。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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