Stochastic dynamic programming for modelling and solving extended multivariate structural models

这项研究计划的目的有三个。首先，我们建议设计一组随机动态规划，用于模拟具有多个上市公司的结构设置。每家公司都假设了一种扩展的资产负债表结构，其中1-任意的公司债务组合，2-多个资历级别，3-嵌入公司债券的选项，4-税收优惠，5-破产成本，6-重组过程。接下来，我们建议以最有效的方式来解决和实现我们的随机动态规划。这一步骤导致了对上述公司证券的估值。基于近似最大似然法和伪极大似然法的模型估计步骤取决于IVADO赠款申请的成功(蒙特利尔大学)。融资决定将于2017年11月做出。建模、评估和评估步骤会产生可操作的和现实的结构模型。本研究计划的最后部分包括对北美上市公司的数字和实证调查。鉴于Leboeuf和Pinnington(2017)(加拿大银行)发现加拿大公司正在变得更具风险，计划在存在传染效应的情况下对加拿大公司及其关联的美国公司进行信用风险比较研究。公司违约导致公司债权持有人的价值损失和公司工人的职位损失。因此，企业信用风险模型对市场参与者很有用，因为它们有助于防止财务困境及其不利事件。本研究项目的创新之处在于，它考虑了1-具有多个有形/无形公司证券和重组过程的扩展资产负债表结构，2-各种多变量马尔可夫-L过程下的有效随机动态规划，以及3-加拿大上市公司的经验和数字信用风险调查。设计、求解和实现我们的有效的随机动态程序是根据结构框架下的上市公司的数量来讨论的，特别关注中维状态空间。使用了近似和神经动态规划。预期收益主要包括在JCR数据库的可靠学术期刊上发表的一组文章。加拿大上市公司的信用风险调查将成为一次科学会议的主题，该会议将聚集学者、学者和专业人士讨论这一问题。

The aim of this research program is threefold. First, we propose to design a set of stochastic dynamic programs for modelling structural settings with multiple public companies. Each firm assumes an extended balance-sheet structure with 1- an arbitrary corporate-debt portfolio, 2- multiple seniority classes, 3- options embedded in corporate bonds, 4- tax benefits, 5- bankruptcy costs, and 6- a reorganization process. Next, we propose to solve and implement our stochastic dynamic programs in the most efficient way. This step results in the valuation of the above-mentioned corporate securities. The model-estimation step, based on approximate- and pseudo-maximum likelihood, is subject to the success of an IVADO grant application (University of Montreal). The funding decision is in November 2017. The modelling, valuation, and estimation steps result in operational and realistic structural models. The last part of this research program consists of a numerical and empirical investigation of North American public companies. Given the finding of Leboeuf and Pinnington (2017) (Bank of Canada) that Canadian firms are becoming riskier, a comparative credit-risk study of Canadian firms and their associated American firms is planned in the presence of contagion effects.A corporate default results in a loss of value for the firm's claimholders and a loss of positions for the firm's workers. Corporate credit-risk models are thus useful for market participants in that they help preclude financial distress and its adverse events.This research program is innovative for it considers 1- an extended balance-sheet structure with multiple tangible/intangible corporate securities and a reorganisation process, 2- efficient stochastic dynamic programs under various multivariate Markov-Lévy processes, and 3- an empirical and numerical credit-risk investigation on Canadian public companies. Designing, solving, and implementing our efficient stochastic dynamic programs is discussed depending on the number of public companies underlying the structural framework with a special focus on intermediate-dimensional state spaces. Approximate- and neuro-dynamic programming are used.The expected benefits consist essentially of a set of publications in solid academic journals of the JCR database. The credit-risk investigation of Canadian public companies will be the subject of a scientific meeting that will bring together scholars, academics, and professionals to discuss this issue.