Stochastic dynamic programming for modelling and solving extended multivariate structural models

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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.