Optimal Lending and Investment with Default Risk

人们越来越关注违约风险及其对贷款合同结构的影响。违约和违约似乎是相当普遍和昂贵的各种情况下，从公司贷款，主权债务和机会主义退出行为。在所有这些情况下，融资代理人（贷款人、公司）可能无法分享投资回报以支付其成本，而借款人/工人可能会为其资本和资源找到其他用途。在存在违约风险的情况下，合同应该如何设计？违约风险如何限制贷款和投资？这些是本提案所处理的主要问题。更具体地说，本提案的目的是考虑在存在违约风险的动态环境中的最佳融资。我们考虑的环境中，默认/低效分离发生的最优合同下的正概率。融资受到自愿还款的限制：借款人可以在任何时候离开，寻找一些外部机会。外部机会的价值是随机的和私人的信息。这是与现有文献的关键区别，并意味着违约实际上发生的概率为正的最优合同的一部分。因此，我们的方法提供了内生违约的契约理论基础和影响的时间配置的借贷约束和投资。我们没有特别的假设合同，但施加的约束所产生的代理人的私人信息和缺乏承诺。我们的模型允许一些不同的经济解释。最明显的是公司融资，贷款人是从事投资项目的企业家，借款人是寻求为该项目融资的银行。或者，也可以将该模型应用于人力资本投资和在职培训。在这种情况下，借款人是在公司工作时积累技能的工人。该公司帮助为这项投资提供资金，但担心留住工人。或者类似地，一个研发实验室的研究人员可能会放弃从实验室开发的想法中获益。最后，这一模式可适用于国际环境，将借款人解释为寻求从外国投资者那里为其政府支出，包括公共投资提供资金的主权政府。在所有这些情况下，违约/分离的风险限制了投资的可能性。反过来，资本的积累可能会对外部机会产生影响，从而对违约风险产生影响。一个最优的动态合同考虑这种最优的权衡随着时间的推移。我们提出的方法具有额外的优势，提供了一个非常易于处理的框架。最优动态契约是一个问题的解决方案，可以很容易地描述为简单的情况下，很容易计算更一般。这与现有的动态模型的违约，被广泛使用的主权债务文学-这是非常难以描述和进行非常高的计算负担。broaderimpactThe研究建议提供了一个新的和非常听话的框架来研究问题的贷款和投资的违约风险。有大量的文献，从金融，消费者理论，劳动经济学和国际经济学的模型适用。因此，我们的研究将提供一个理论框架，看看在这一领域的证据。此外，它将有助于更好地理解合同的结构，以减轻违约风险，同时利用投资机会。从方法论的角度来看，建模方法（连续时间/泊松到达）在动态合同文献中也是相当新颖的，并被证明比标准（离散时间）方法具有相当大的优势。在这一领域的未来研究将发现这种方法是有用的。

Intellectual meritThere is growing concern about the risk of default and its implications for the structuring of lending contracts. Default and breach of contract appear to be quite pervasive and costly in a wide variety of situations ranging from firm lending, sovereign debt and opportunistic quit behavior. In all these cases, the financing agents (lenders, firms) may fail to share returns to the investments to cover their costs while the borrower/worker may find alternative uses for their capital and resources. How should contracts bedesigned in the presence of default risk? How does the risk of default constrain lending and investment? These are the main questions addressed in this proposal. More specifically, the purpose of this proposal is to consider optimal financing in dynamic settings in the presence of default risk. We consider an environment where default/inefficient separations occur with positive probability under the optimal contract. Financing is constrained by voluntary repayment: the borrower can, at any moment, walk away for some outside opportunity. The value of the outside opportunity is random and private information. This is the key difference with the existing literature and implies that default actually occurs with positive probability as part of the optimal contract. Our approach thus provides contract theoretic foundations for endogenous default and implications for the time profile of borrowing constraints and investment. We place no ad hoc assumptions on contracting, but impose the constraints arising from the agent's private information and lack of commitment. Our model allows for a few different economic interpretations. The most obvious is the financing of a firm, where the lender is an entrepreneur undertaking an investment project and the borrower is a bank seeking to finance this project. Alternatively, one can apply the model to human capital investments and on-the-job training. The borrower in this case is a worker accumulating skills while working at a firm. The firm helps finance this investment but is concerned about retaining the worker. Or similarly, a researcher in an R&D lab that may quit benefiting elsewhere from ideas developed in the lab. Finally, the model can be applied to an international context by interpreting the borrower as a sovereign government seeking to finance its government spending, including public investments, from foreign investors. In all these situations, the risk of default/separation constrains the possibilities of investment. In turn, theaccumulation of capital is likely to have an impact on outside opportunities and consequently on default risk. An optimal dynamic contract considers this optimal tradeoff over time. The approach we propose has the additional advantage of providing a very tractable framework. The optimal dynamic contract is the solution to a problem that can be easily characterized for simple cases and very easily computed more generally. This contrasts with existing dynamic models of default that are extensively used in the sovereign debt literature- that are very difficult to characterize and carry a very high computational burden.Broader impactThe research proposed provides a novel and very tractable framework to study problems of lending and investment with default risk. There is a large literature ranging from Finance, consumer theory, labor economics and international economics to which the model applies. Our research will thus provide a theoretical framework to look at evidence in this area. Moreover, it will help better understand the structuring of contracts to mitigate default risk while taking advantage of investment opportunities. From a methodological point of view, the modeling approach (continuous time/Poisson arrivals) is also quite novel in the dynamic contracts literature and proved to have considerable advantages over the standard (discrete time) approach. Future research in this area will find this approach useful.