Martin Szydlowski Assistant Professor of Finance 




Publications
On the Smoothness of Value Functions and the Existence of Optimal Strategies, with Bruno Strulovici, Journal of Economic Theory, Vol. 159 (2015)
Abstract: We prove that the value function for the optimal control of any timehomogeneous, onedimensional diffusion is twice continuously differentiable, under Lipschitz, growth, and nonvanishing volatility conditions. Under similar conditions, the value function of any optimal stopping problem is continuously differentiable. For the first problem, we provide sufficient conditions for the existence of an optimal control. The optimal control is Markovian and constructed from the Bellman equation. We also establish an envelope theorem for parametrized optimal stopping problems. Several applications are discussed, which include growth, dynamic contracting, and experimentation models.
Optimal Financing and Disclosure Abstract: How does a firm's disclosure policy depend on its choice of financing? In this paper, I study a firm that finances a project with uncertain payoffs and jointly chooses its disclosure policy and the security issued. I show that it is optimal to truthfully reveal whether the project's payoffs are above a threshold. This class of threshold policies is optimal for any prior belief, for any security, and any increasing utility function of the entrepreneur. I characterize how the optimal disclosure threshold depends on the underlying security, the prior, and the cost of investment. The optimal security design is indeterminate despite the presence of adverse selection. Among others, the optimum can be implemented with equity, debt, and options. Incentives, Project Choice and Dynamic Multitasking
Abstract: I study the optimal choice of investment projects in a continuoustime moral hazard model with multitasking. While in the first best, projects are invariably chosen by the net present value (NPV) criterion, moral hazard introduces a cutoff for project selection which depends on both a project's NPV as well as its riskreturn ratio. The cutoff shifts dynamically depending on the past history of shocks, the current firm size, and the agent's continuation value. When the ratio of continuation value to firm size is large, investment projects are chosen more efficiently, and project choice depends more on the NPV and less on the riskreturn ratio.
The optimal contract can be implemented with an equity stake, bonus payments, as well as a personal account. Interestingly, when the contract features equity only, the project selection criterion resembles a hurdle rate.
Ambiguity in Dynamic Contracts Abstract: I study a dynamic principal agent model in which the effort cost of the agent is unknown to the principal. The principal is ambiguity averse, and designs a contract which is robust to the worst case effort cost process. Ambiguity divides the contract into two regions. After sufficiently high performance, the agent reaches the overcompensation region, where he receives excessive benefits compared to the contract without ambiguity, while after low performance, he enters the undercompensation region. Ambiguity also causes a disconnect between the current effort cost and the strength of incentives. That is, even when the agent is undercompensated, his incentives are as strong as in the overcompensation region, since the principal fears the agent might shirk otherwise. Under ambiguity, the agent's true effort cost does not need to equal the worstcase. I analyze the agent's incentives for this case, and show that the possibility of firing is detrimental to the agent's incentives. I study several extensions concerning the timing structure and the nature of the principle's ambiguity aversion.
Work in Progress
Moving the Goalposts, with Jeff Ely Teaching
FINA 4221: Principles of Corporate Finance (undergrad)  
