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 time-homogeneous, one-dimensional diffusion is
twice continuously differentiable, under Lipschitz, growth, and
non-vanishing 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.
The Market For Conflicted Advice, with Briana Chang
Abstract: We study decentralized markets in which
advisers have conflicts of interest and compete for customers via
information provision. We show that competition partially disciplines
conflicted advisers. The equilibrium features information dispersion and
sorting of heterogeneous customers and advisers: advisers with
expertise in more information sensitive assets attract less informed
customers, provide worse information, and earn higher profits. We
further apply our framework to the market for financial advice and
establish new insights: it is the underlying distribution of financial
literacy that determines the consumers' welfare. When advisers are
scarce, the fee structure of advisers is irrelevant for the welfare of
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.
Abstract: I study the optimal choice of investment
projects in a continuous-time 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
risk-return 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 risk-return 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.
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
over-compensation region, where he receives excessive benefits compared
to the contract without ambiguity, while after low performance, he
enters the under-compensation region. Ambiguity also causes a disconnect
between the current effort cost and the strength of incentives. That
is, even when the agent is under-compensated, his incentives are as
strong as in the over-compensation region, since the principal fears the
agent might shirk otherwise.
Under ambiguity, the agent's true effort cost does not need to equal the
worst-case. 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
FINA 4221: Principles of Corporate Finance (undergrad)