The common justification, in financial theory, for the existence of debt covenants is their use as contractual devices that reduce agency problems between borrowers and lenders. The thesis first examines the extent to which debt covenants alleviate these agency problems, and how they affect a borrower's debt financing decisions. Then, building on recent theories on the costs of bank financing, the dissertation suggests a new economic rationale for debt covenants as instruments that can reduce these costs. The thesis consists of three essays: / The first essay shows that, debt covenants create underinvestment incentives while reducing the overinvestment cost of debt It also finds that the borrower's choice between different contracts with, and without covenants, depends on the magnitude of the agency problems, and the quality of the lender's monitoring technology. / The second essay shows how debt covenants reduce the costs of banks information monopoly. In fact, contingent contracting with debt covenants can be used by banks to precommit against using their informational advantage to hold up borrowers and extract rents, thus giving borrowers incentives to exert greater effort. / The third essay shows that the renegotiation that debt covenants permit, can reduce liquidity risk defined as the risk that a solvent but illiquid borrower is unable to obtain refinancing. It also shows that a debt contract with covenants is similar to a mix of debt contracts with different maturities. / The thesis concludes with a review of the determinants of corporate debt maturity structure, and the literature on corporate reliance on bank financing and suggests future research in this area.

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The problem of credit rationing/borrowing constraint has recently received considerable attention. Individuals who are denied any credit by a financial institution, or who find it difficult to borrow against future incomes, are said to be credit rationed or borrowing constrained in the credit markets. This dissertation tries to identify the circumstances under which individuals may be rationed (or not), and analyses the actions undertaken to overcome future constraints. Chapter 2 analyses the problem of credit rationing as it arises in equilibrium, when borrowers differ with respect to their demands for loans. It is shown that if the principal can costlessly observe the agent’s type, then (i) the agents who meet the collateral requirements are not rationed in the sense of Stiglitz-Weiss (1981), (ii) the agents who do not meet the collateral requirements are rationed in the sense of Jaffee-Russell (1976). We further show that if the principal cannot distinguish between different agents, then the previous rationing results still hold in the second best contract which is pooling : agents of different types pick the same contract. Chapter 3 analyses the problem of credit rationing as it emerges in a dynamic setting, when a renegotiation of the original contract may be undertaken. It is conjectured that (i) the principal uses the information revealed about an agent’s type at the time of first repayment, to design future contracts, (ii) the agents who show consistently honest behavior are never rationed, (iii) the agents who showed dishonest behavior impose a negative externality on the agents who were honest; they are rationed in later periods. Finally, in chapter 3, we analyse the role of an exogenously imposed borrowing constraint prompting the individuals to change their life-cycle decisions. This chapter provides an explicit link between human and non-human wealth by making income endogenous through investment in human capital. The chapter also discusses the econometric aspects of the problem: the possible empirical work that can be undertaken in the future using a micro data set. / Ph. D.

We consider the problem of optimization and decision-making in various settings involving complex systems. In particular, we consider specific problems in decentralized finance which we address employing insights from mathematical finance, in course-mode selection that we solve by applying mixed-integer programming, and in social networks that we approach using tools from graphical game theory.In the first part of the thesis, we model and analyze fixed spread liquidation lending in DeFi as implemented by popular pooled lending protocols such as AAVE, JustLend, and Compound. Empirically, we observe that over 70% of liquidations occur in the absence of any downward price jumps. Then, assuming the borrowers monitor their loans with exponentially distributed horizons, we compute the expected liquidation cost incurred by the borrowers in closed form as a function of the monitoring frequency. We compare this cost against liquidation data obtained from AAVE protocol V2, and observe a match with our model assuming the borrowers monitor their loans five to six times more often than they interact with the pool. Such borrowers must balance the financing cost against the likelihood of liquidation. We compute the optimal health factor in this situation assuming a financing rate for the collateral. Empirically, we observe that borrowers are often more conservative compared to model predictions, though on average, model predictions match with empirical observations. In the second part of the thesis, we consider the problem of hybrid scheduling that was faced by Columbia Business School during the Covid-19 pandemic and describe the system that we implemented to address it. The system allows some students to attend in-person classes with social distancing, while their peers attend online, and schedules vary by day. We consider two variations of this problem: one where students have unique, individualized class enrollments, and one where they are grouped in teams that are enrolled in identical classes. We formulate both problems as mixed-integer programs. In the first setting, students who are scheduled to attend all classes in person on a given day may, at times, be required to attend a particular class on that day online due to social distancing constraints. We count these instances as “excess.” We minimize excess and related objectives, and analyze and solve the relaxed linear program. In the second setting, we schedule the teams so that each team’s in-person attendance is balanced over days of week and spread out over the entire term. Our objective is to maximize interaction between different teams. Our program was used to schedule over 2,500 students in student-level scheduling and about 790 students in team-level scheduling from the Fall 2020 through Summer 2021 terms at Columbia Business School. In the third part of the thesis, we consider a social network, where individuals choose actions which optimize utility which is a function of their neighbors’ actions. We assume that a central authority aiming to maximize social welfare at equilibrium can intervene by paying some cost to shift individual incentives, and that the cost is upper bounded by a budget. The intervention that maximizes the social welfare can be computed using the spectral decomposition of the adjacency matrix of the graph, yet this is infeasible in practice if the adjacency matrix is unknown. We study the question of designing intervention strategies for graphs where the adjacency matrix is unknown and is drawn from some distribution. For several commonly studied random graph models, we show that the competitive ratio of in intervention proportional to the first eigenvector of the expected adjacency matrix, approaches 1 in probability as the graph size increases. We also provide several efficient sampling-based approaches for approximately recovering the first eigenvector when we do not know the distribution. On the whole, our analysis compares three categories of interventions: those which use no data about the network, those which use some data (such as distributional knowledge or queries to the graph), and those which are fully optimal. We evaluate these intervention strategies on synthetic and real-world network data, and our results suggest that analysis of random graph models can be useful for determining when certain heuristics may perform well in practice.